SCIENTIFIC ABSTRACT LADYZHENSKAYA, O.A. - LADYZHENSKIY, L.A.

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• Collection: Scientific Abstracts
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• Document Creation Date: November 2, 2016
• Document Release Date: June 20, 2000
• Sequence Number: 6
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

22407
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Quasilinear elliptic equations ... C 111/ C 333
u(x x ) of the regular variational problem concerning the
minimum of n
1(u) F(x,u,it ) dxI ... dx n
under the condition U/S - 'P(s)-
Let 11 be a bounded domain of the x = (Xjq..., X n) in the Euclidean
En1 41 -- 'strictly interior subdomain of 4 ; C 110 (11 ) the set of
all functions u(x) which are continuous with respect to xk in the
open R together with the 1 first derivatives; let
-f
lul zax ID kU(x)l
02
V-M 0
be the norm. Let C, (EQ be the set of all functions from.C
for which IOU 1,0
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QUaBilinear elliptic equations ... C 111/ C 333
blu(x.+h) - D 3. u 00 ei) 1
max
u
x,x,th C h Joe
1hi >0
C4
is bounded. The norm iss lul, 1 1 Ul Cl'o (WA. 2~ D u. Let C
be the set of all functions continuous in fL I u1 C a - max I U(X)
1 '1 0 XF-fL
Let W m(j).) and WM(A) be defined as usual (see V~ J. Smirnov (Ref,2:
Kurs vysshey matematiki Course in higher mathematicsi t. IV, M.,
Fizmatgiz, 1959)). W lu~x)j for u E W mM) is defined to be vrai
~t lu(x)l. Let D,(a be the class of the functions u(x) which in
possess 1 - 1 derivatives with respect to x,
derivatives D 1-1 ,, and for which the
u possess a differential in every point of R.Let
01(Q) be the class of the v(yit .... ym) E D,(Q), the 1-th derivatives
of which are bounded in every bounded domain of the YM*
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22407
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Quasilinear elliptic equations ... G Ill/ G M
Let 0 (1) be the class of the functions measu-vable and
bounded in every finite domain of the y1g...9 Ym. The statement
11 the norm 1-1 is estimated by the data of the problem"' means that
the estimation is poasible by the constants which occur in the
conditions which are fulfilled by the problem. ItkOul) denotes
positive nondecreasing and vk(jul) positive nonincreaoing functions
of Jul defined on EO , CV) and finite for all finite 1u1. The state-
merit "the function f(xip ... , XU, P11 Pn) , X has the
order of growth m in p 2 says that max
SPk If (X'U'Pk)
2 =/2 X E fL
,/-,,0uMP +1) The boundary S possesses the property ~A~, if
there are a '> 09 0 < 0 V 1 such that for every sphere K s with
center on S and radius 3 -5-a it holds
mes (1 - E)) mes K(5
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22407
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quasilinear.el-liptic equations ... 0 Ill/ C 333
S belongs to C1, if it can be covered by a finite number
of open pieces, -fi; :-qu~at'io'ns of which belong to C
Theorem I. Let u(x:) be a bounded generalized solution of
xl(u) = -a (ai(X,U,u )) + a(x,u,u ) . 0 (29)
~a xi xk xk
i. e. u GW 1(fQ,jul.!~- M and u(x) is assumed to satisfy the.inequality
m
i(xqufu 31. ) I)X - a(xsuu )7)j dx - 0 (30)
'k i xk
for a"itrary al Let furthermore mx I ux MI
~ (-x) GW.(S1
a 0 (11~a -A En) and a (x, u, Pjr) e oo (fil-)cf: ). Let
i(x'u'Pk) G 1 1 1 n
Dai(X+Tht VP v xk ) n 2
,av fj >,'Vl(lvl)92 OVvl) 7-9,
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22!407
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Quasilinear elliptic equations ... C 111/ C 333
for v(x) - (1 u(x) + C u(x + h), -c e E oo I , X, x + h
The norm JUIC 0, for arbitrary Sj,' C 11- is then
estimated by JUIC 1'0 If, moreover, S G 02,o and 'F(s)
U/S C- C2,o (a), then Jul, 1, gl )is estimated by luic 1,0 (SL) and
1'?1C 2,o (s) . If a, and a belong as functions of their arguments to
CI- I "C4- (1'-> 2) or to C1-2, OL, on every compact, while 8 and 'P(s) belong
to C1 "C then 1u 1C ",41-L ) is estimated by I u IC and by the
1, _ 1,0
data of the problems
The equation (29) is said to belong to the class if it satisfies
for arbitrary the conditions
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I
22407
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Quasilinear elliptic equations ... 0 ill/ C 333
it- 2 n
(1u, )(P2 + 1 27 7 2 ,., -e
vi 1 1 ,i5(xju,]) k) ~t~ I u
m-2 2
(p 2 + 2 (16)
a(x,us,P 0 U (17)
k) I -t-- 4-L'2, (1 upm +1-t'3
and,for large p
ai (x . u I'Pk) Pi >,- v 10 u I ) pm (M (31)
2 n 2
where;p - iml Pi
Theorem II. For am. arbitrary equation (29) of the class the first
boundary Yalue problem with the boundary condition U/S = C~s) has at
Uard 7/45

22407
S/()42/61/016/001/001/007
Quasilinear elliptic e4ustiOns ... C Ill/ C 333
-Ja )' if the maxim&
least one solution in the class C 2p'- fL ) %
I
of the absolute values of the solutions u(x,rr of the boundary
value problems
M IG (u) -= (l - /C ) M
ku) + 'CM I (u) - 0' U/S -'rcr Eo' 11
o
are uniformly boundod, whe-re. %(u)=-2- Fo (u,u - F~(U'u and
0 X
x
. ux.
1c
I
) - kl+P 2)m/2 + u2 , The coefficients 3. a
Fo(u'p
) and a(%,u,p
(x'u'P
k
i
k
k
must belong to C 29o4 and C1,,,-respectively as functions of their
arguments on every compact. The boundary 9 and T ka) must belong to
C

Theorem III is a special case of theorem II.
Theorem IV. The propositions of theorem II are maintained, if all
conditions except (31) are satisfied and if moreover the orders
of growth in p of the functions
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Quasilinear elliptic equations ... C 111/ C 333
,;~2ti(X'U'pk) 2ai(X,U,Pk) and 'Ja(X,U,P) -- not greater
Z)pj ~)u ~ U2 ~)u
than v -,Z - F,Iqiz-4-Ea:ad m -E , where F- > 0 is arbitrary.
Oneorem V. Let u(x) e Wm(-()-) be one of the generalized dolutions
of the variational problem
inf I(u) - illf f(xou,-a Xk ) dx, dx -, dxI ... dx,, (2)
U/S ~-f S) (3)
with the additional condition that all comparison functions are in
the absolute value aot greater than a constant M >, max Jul . This
solution belongs to Col.,-(J')) , c;,/- -> 0, if S
F (x I u'Pk) G C 1 E- N' M
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22407
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Quasilinear elliptic equations C Ill/ C 333
;;?: (Jul) pm f or p 5,-:7 1
?Pi(xsu'Pk) Pi \)I
and
U.
P F Pi (x,u,pk) +1 F u(xpuppk) ti u1 ) (p' + 1)
UndL-r the same assumptions on F, every bounied u(x) E W which
m
gives I a stationary value belongs to U Otol- (D). If, moreoverp the
boundary of (I satisfies the condition kA), and if T(s) can be
continued in SL so that T(X) G 01( a), then in both cases it holds
U (X) e C 0 , "jfl-) -
Theorem VI. If only the natural restrictions 1.) - 4.) are satilfied
for F(X,U,P, ), then every bounded generalized solution -a(x)G 1QSL)
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Quasilinear elliptic equations ... C Ill/ C 333
of the variational problem (2), (3) belongs to C k.c4- (SI), L~> 0, if
F(x,u,p ) as function of its arguments belongs to C k > 3 on
k k
every compact. If, moreover, B e C and (f e C, 2 !~- 1 k,
11 cle-
then u(x) belongs to cl,.e-(-ft ) too. As natural restrictions for
F(x 'u'Pk) there are denotedt
I.) VIOUMP 2 + 1)M/2 F(x,u,p,,) _!5 ei(juj)(P2 + 1),/2
2.) The Euler equation for F(X J'u"Pk ) is uniformaly elliptic.
((I) is called uniformly elliptic# if (16) holds).
3-) F is sufficiently smooth, where the differentiation of F and of
its partial derivatives with respect to Pk reduces -the order of growth
of F and of the derivatives mentioned at least by 1, while,the
differentiation iath respect to xk and u- does not increase the-se orders
of growth.
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22407
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Quasilinear elliptic equations ... 0 111/ C 333
For all sufficiently large p it holds
Fp.(X'U'Pk) Pi >1 V 2(lul) P' -
I
The given theorems are the main results of the paper; 25 theorems
and 11 lemmata are proved.
The author mention: V. J. Kazimirov, A. G. Sigalov, A. J. Koahelev,
G. J. Shilova, S. L. Sobolev, V. J. Plotnikov, A. D. Aleksandrov,
A. V. Pogorelov, Ye. P. Sen'kin, J. Ya. Bakellman.
There are 16 Soviet-bloc and 25 non-Soviet-bloc references. The
four must recent references to English-language ublications read as
follows: L. Kireaberg, Estimates and existence of solutions of
elliptic equations, Commiln. Pure and Appl. Math. 2, 30956), 509-
531;
Card 12/13

2240
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Quaailinear elliptic equations C 111/,C 333
J. Bash, Continuity of solutions of par&bolic and elliptic equations,
Amer. Journ. lath. 809 No- 4 (1958)y 931-954; R. Finn afLd D. Gilbarg,
Three-dimensional snub onic flows, and aEiymptotic estimates for
elliptic partial differential equations, Aota math. 2-8 (1957),
265-296; C. B. Morrey, Second order elliptic equations in several
variables and Hblder Continuity, Math. Z- 1-2 (1959), 146-164.
SUBMITTED: July 12, 1960
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23799
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C III/ C 222
AUTHORSs Ladymbenakeya, 0. A., aid UralltBeva, N. N.
TITLE8 Differential properties of bounded generalized solu
tions to n-dimensional quasilinear elliptic
equations "d var4.ation groblems
PERIODICALs Akademlya nauk SSSR. Doklady, v.. 138, no. 1, 1961,
29-32
-TFJVfs The authors investigate the equation
n-
(a (X,,U,U a (.-x, U, U0
4
vkere a. ror& a are measurable functionti sati-ifying
P)
(2)
ai(XQUVP P; >, v P" u
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23?9!~
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Differential propert' as of 0 ill/ 0 222
.1
where a ,t- I utd n? p 2 Let besides the coudition
2
1: U, (!+P)""" ~U I+P)m
3
2
p +,." P~
be satisfied incidtntally, where (1) is monotone naxiAareaeing,
(-/.(t) -- mono-tone non-decreasing, t) and t) > 0, t :;. 0,.
A function u(x) e-,.W I (f~) for Vhich
dx
I (u, a. (X,Vyu a(x,upu 0 (4)
[ i x Ixi x
holds for every bounded functlon of V is called a generalized
Card 2-K-

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Differential.properties of ... C 111/ C 222
solution of (1).
Lemma ii For the bounded generalized solution u(x).of (1) there hold
the.inequalities
:Amdx (5)
,/2
-R+Mk- u I mdx 4 c od/2
o, (6)
where KM 2.s an arbitrary sphere of' radius ~ in-0 . and the constant
- depends only on eldmax I u~), -4(me,,x !u ) of (2).
Lea,ma 2: Every bounded generalized 'FlOlUtiGn u(x) of (1) with &;~-, 2
satisfies
m .2 a- 2 ,12
L) 'r dx a dx (7)
every
bounded of
where the constant a depandsonly on
for
/.,4x!~kx I uj ) and -, (mV- u, of (2).
Care 3 /C

09
S/020/6-,/138/001/003/023
Differential properties of C !!I/ C 222
Lemma 2's If b(x):;~O, and if for every :x 0 andyCll it holds
."X-Y:.
bM(x,)dx c, > 0, 1 e m ir- 2 then it holds
bp 2 2'~M bm- 2 1"2
J, dx 15 dx
(8)
where T is ~an a~rbitrary bffmr&vd f-anction of I(K (?)), and the
constant c depends only on c 1~,1114M.
From lemma 21 it follows that lemma 2 holds also for 1,!9: m 2.
Theorem is The uniqueness theorem an the small holds for a bounded
generalized solution U(I Of (~O i, e.; two bounded generalized
solutions UI(x) and ull(x~ being equal on the surface of K(s) are
identieal,:Ln K(s) if only the radius is smaller than a eartain
number whi oh i s de t ermined by ev; (mex u 1) u" );) and .; (max ~ u Iu
of (2) and (3).
Theorem 2: If (2) and (3) are satisfied then every bounded generalized
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Differential pxopert:Lse. of ... C Ill/ C 222
solution U(x)~ of (1)'has generalize&- setond derivatives and satisfies
(1) almost everywhere. For this solution it holds
VujM+2 + (1 +1 .Vul )13-2 U2 dX < a (10)
x x
i
where A is an arbitrary-strongly inner subregion of if S
and 1P-U/s are two times continuously differentitble.thdn (10)
holds for A too.
Let J(U) A F(xqu'ux ) dxIdxA 1~ (12)
Theorem 31 Every bounded u(x) of W 2(A) for which
"rj(u) tF (Xququ ) + xa9 dx - 0 holds for every bounded
-Jl Uxi x xi
01
(.rQ,
,q(x)-,E Ta
belongs Ck,',~ if F(xgu,pj) as a function
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Differential properties of ... C 111/ C 222
of all arguments belongs to "; k,r-f and satisfies oily.the "natural"
assumptions of (Ref. Is 0. A. Ladyzhenskaya,,N. N. Uralltseva '. DAN
135, no. 6(!960); Ref. 2s 0. A. Ladyahenskaya, N. N. Uralltsevaq Usp.
mate*. nauk,, 16, no. 1 (1961)).
V
There are 4 Soviet-bloc and 2 non-Soviet-bloo references.
ASSOCIATION: Leningradskiy gosudarstvennyy universLtet imeni A. A.
Zhd&nova (Leningrad State University imeni A. A.
Z4 ianov)
PRESENTED3 December 24, 1960, by If. J. Smirnov, Academician
SUBMITTEDs December 20, 1960
Card 6/6

LADYZHENSKAYA, O.A.; URAPTSEVA, N.N.
Bou-darv value Droblem for lint-ar and quasi-linear parabolic
equations. Dokl. AN SSSR 139 no-3:544-547 J1 '61 (MIRiL 14:7)
1. Leningradskiy gosudarstvennyy universitet im. A.A. Zhdanova.
Predstavleno akademikom V.I. Smirnovym.
(Boundary value problems)
(Differential equations, Linear)

LADYZHENSKAYA, O.A.; URALITSEVA, N.N.
Regularity of generalized solutions of quasi-linear elliptic
ecuations. Dokl. AN SSSR 140 no.1:45-47 S-0 161. (YJRA 14:9)
1. Leningradskoye otdeleniye Hatematich6sYogo instituta im. V.A.
Steklova AN SSSR. Predstavleno akademikon V.I.Smirnovym.
(Differential equations)

TAOU.MSIOAM, 0. A.
"Quasilinear equations of elliptic and parabolic types"
report submitted at the Intl Coaf on Mathematics, Stockholm, Sweden,
15-22 Aug 62

~A~~~~
ItSur les equations differentiel las quasi lineaires d6 type elliptique
et parabolique."
Report to be submitted for the International Colloquim on Partial
Differential Equations (CMIS) Paris France, 25-30 June 1962.

33628
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-5 6-0 0 B112/B108
AUTHORS~ Ladyzhenskaya, 0. A.,and Uralltseva, N. N.
TITLE: Boundary value problem for linear and quasi-linear parabolic
equations. 1.
PERIODICAL: Akadimiya nauk SSSR. Izvestiya seriya Matematicheskaya, v.
26, no. 1, 1962, 5-52
TEXT: For linear parabolic equations of the form
Lus;'u (9/3xi)(aij(x,t)ux + a,.(x,t)u + f b.(x,t)u
+ta():,t)u + f(x,t) - 0 j(x,t))
with unboimded coefficients, estimates of the HUlder norm of the solutions
and of their derivatives are derived. For the solutions of general quasi-
linear parabolic equations
f,u Z ut - (9/?,xi)(a,(x,t,u,u xk )) + a(x,t,u,u Xk 0
"with a divergent right-hand Bide'lp apriori estimates are obtained. By
means of these estimates it is demonstrated that the first boundary value
Card 1/2

33628
S10381621026100110011003
Boundary value problem for... B112/B108
problem for such equations can be solved "in the large". All results are
new inclUBi7e that for the case of a single spatial variable. The condi-
tions under which the apriori7'estimates are obtained and under which the
solvability "in the large" is demonstrated are not only sufficient but in
a certain sense also necessary. There are 37 references: 21 Soviet-bloc
and 16 non-Soviet-bloo. The four references to English-language publica-
tions read as follows: Nash J., Continuity of solutions of parabolic and
elliptic equations, Amer. J. Math., 80 (1958)9 931-954; Friedman A.p On
quasi-linear parabolic- equations of the second orderg J. Math. and Nech.,
7, No- 5 (1958), 771-791; 793-809, Morrey C. B., Second order elliptic
equations in several variables and Hblder continuity, Math. Z.. 72 (1959),
146-164; Friedman A., Boundary estimates for second order parabolic
equations and their applications, Journ. Math. and Mech., 7, No- 5 (1958),
771-791.
SUBMITTED: May 18, 1961
Card 2/2

5/038/62/026/005/003/003
B112/B186
AUTHORS% Ladyzhenskaya, 0. A., and Uralltseva, N. N.
TITLE. Boundary valae problems for linear and quasi-linear
parabolic equations. II
PERIODICAL: Akademiya nauk SSSR. Izvestiya. Seriya matematicheskaya,
v. 26, no- 5, 1962, '753-760
TEXT: The first boundary value problem for quasi-linear parabolic
equations n
Xu M u t da i(x,t,u,u, )/dxi +,a(xttlu,ux 0 (1)
k k
with "divergent main part" i's considered f-rom a global point of view.
Local results concerning such equations have been obtained in the fitst
'part of this paper (Izvestiya Ak. nauk SSSR, seriya matemat., 26 (1962),
5-52). Global estimates ofIVul and of the Hdlder norm of u x are
derived. From these estimates, the existence of classical solutions is
"'Card 1/2

Boundary value problems for...
S/038/62/026/005/c)03/003
B112/B186
proved for bounded and unbounded domains and, in particular, for
Cau,chy's problem. Special attention is paid to the theorem of existence
at an arbitrary growth, with r,~:spect to problems of a"surface hydro-
dynamics.
SUB14ITTED: February 20, 1962
Card 2/2

02/()22
/001/0
5/02OP" /1%41
qeGOn
Oqs
OTO
'Oleo Ts
enOLSY S ,Ue 'P'ro %,h8 Or';Oe 19 1962.1
Of no.
~Udsrl von,
bo eqIs
ordeT 55SIL - 01
deVLJl 96 ,,Iae 'Proolels, t sill (2)
WIWI
olio b0
V, T~Le Vs-rs-b 11 11 01 su%IL ctious"
tri.
T US c net /09
t i, 01 ,,, genuine 'b i. 'o
Oe fo ())7/ 1A1 -:r/O
,Te66 t t 'al 0)
7, '01051
r
19 SVY
1% ell
ASSL 4. t
im. A. Zhdanova
PRESE Or "Ini A. A. Zhdanov)
SUBMI7 Cs rd, 1/2 SmirnOvp Academician
Card 2/'

S/020)'62/147/001/002/022
B1 12/11102
AUTHORSt Ladyzhenskaya, 0. A., Uralltseva, X. N. -
TITLE: The first boundary value problem for quasilinear second-
order parabolic equations of the genera.1 form
PERIODICAL: Akademiya nauk SSSR.. Doklady, v. 147, no. 1, 1962, 28-30
TEXT. The parabolic; boundary value problem-
n
t - . T- aij(x,tlu,u x )U x x + a(x,tju,uX 0,
19J-1 k i j k
UIS - 0, ult.0 - ?(X)--
is comsidered under the following genuine ;Irestrictionalli
(a) a(xltpu,O)>.,-b1u2 _ b2g bi - cc,nst>,O,
i aij(x)tVu9O)tiij >11 0
for (x,t) E,~T - E-to 4 t 4~3T=) and any u;
Card 1/2
(1)
(2)

S/020/62/147/001/002/022
The first boundary value problem... B112/B102
(b) V (I a 1) 0 + W-1 < ali (x, u, pk) tit/ < ji (I u+ p)m-2
a I + + + P) 2+
(III apk dxk au
+
aPk + 03 4- + P), < IL (I U+ P).,
1 1 (1 dxk and any u, For the
where m is an arbitrary number, for (X,t) e ~T Pk'
general equation (1), the same solution estimates are derived as in previous
papers for a parabolic equation "with divergent principal part"
(of. 0. A. Ladyzhenskaya, DAN, 107, No. 5 (1956); Tr. Mosk- matem. obshch.,
7, 149 (1958), and 0. A. Ladyzhenskaya, N. N. Ural't8eva, UXN, 16, no. 1,
19 (1961)). The derivation departs from the previous ones.
ASSOCIATION: Leningradskiy gosudarstvennyy universitet im- A. A. Zhdanova
(Leningrad State 'University imeni A. k. Zhdanov)
PRESENTED; May 21, 1962, by V. .1. Smirnov, Academician
SUBMITTED: May 17, 19062
Card 2/2

LADYZHEMKAYA. . URALITSEVA, N. N.,
On possible extensions of the concept of solution for linear
and quasi-linear second-order e3-liptic equations. Vent. I= IS
no.1:10-25 163. (MIRA 16:1)
(Differential equations)

45652
P/03 63JO27/001/004/004
AUTHOM. -,-Ladyzhen,,sk,,a.,Y,,a,, 00, An. and Uralltsevap, So No
TITLE: -Boundary-value problem for linear and quasilinear
eqpat.ione.and systems of the parabolio type. III
PERIODICAL: Akademi inauk SSSR. Izveetiya. Seriya matematiohookayat
ya
yc 27 1 no. 11 19631 161-240
TEXT: C.eneral,quabilinear equations
.0 (x., 1, U. u..) &h.., +:a'(xt to'U, U.1%) 0.
a
parabolic systems.
ul d au (X,' t) U;+ Y. aim (z,.t) 0 + ti (x, j) +
iF,
x
bj'- (x. + b- (x, t) e + 0' 1 =1*0 .... N, (2)
a' (x, t, u
aq (z, u"~) u.
Card 1/2

LADYZHENSKAYA, O.A.; URALITSEVA, N.N.
I ~oldeiw continuity of solutions and their derivatives for linear
and quasi-linear elliptic and parabolic equations. Dokl. AN SSSR
155 no.6:1258-1261 Ap 164. (MIRA 17:4)
1. Leningradskoye otdeleniye Matematicheskogo instituta, im. V.A.
Steklova AN SSSR. Predstavleno akademikom V.I.Smirnovym.

'ACCESSION fift:
i
AP403402~ B/0020/64/155/C,06/1258/3-261
4UTHOR: La"herjsMya., 0. A.; Uralltsevap N. N.
TITLE: On H81der-continuity of solutionso and derivatives of solutionsp of linear
and quasi-linear equations of elliptic and parabolic type.
tSOURCE: AN SSSR. Dok3.ady*p V. 155, no. 60 1964, 1258-1261
TOPIC TAGS: partial differential equation, second order, elliptic equation,
.e;L11pt1c system, parabolic equation, parabolic system, generalized solution
;ABSTRACT: In a series of (seven) earlier papers the authors have studied equations
Of elliptic or parabolic type, of the forms
Zu (al, W u., + a, (x) u) + b, (x) u., + c (x) u(x),
X?u L - -L (all (.x. 1) u., 4- at (x. 1) W 4- b, (x, 1) u,,, + c (x, 1) u(x, 1),
& ox,
Z3u z~~ You a--- ul -all (x, t, a, US) U"tZ, + a (X. 1, U, a.) 0 (6)
(a, (x, u, u.)) + a (x, u, u.) (3
u (a, (x, 1, u, u,)j 1+ a (x, 0,(+IX,u all (x, U, U.) UZIX/+a (X U, 0. (5)
Card 1/4

ACCESSION NR: AP4034025
and certain systems of such equations. One of the main objects of their vork van
investigating-the H81der-continuity of the solutions and their derivatives., as well
.as getting estimates for their H81der norms in terms of-consUnts depending on the
coefficient functions. By constructing special examples, they have shown that in
a certain sense, their results cannot be improved. Assuming that the solutions
under consideration are bounded and have a certain degree~of-smoothness, it was
shown that every solution u of equations (1) - (4) as weli as each uxtbelong to a
certain class B; the gradient with respect to x of every solution of ) or (6)
.belongs to a certain class BN. (A function belongs to such a class if it satisfies
certain inequalities involving free parameters.) Then it was proved that the
functions in the various B classes are H81der-continuous and that their 1181der norm
can be estimated in terms of the numerical parameters defining B. The object of
this paper is to present a shorter method of proof., by-passing the study of the
B-classes. The reasoning is based on lemmas from the earlier papers and a nev
lemmst . concerning functions in the class WJ (KO., where K2 = I (x) !!:- 2 ]. Since
the results are those which were presented earlier., they are not re-stated here.
InBteads the method is illustrated on the example
Ut- a (all (X, t) U'J)0 (7)
Card 2/4

ACCFSMCN NR: AP4034025
to vhich corresponds the Integral Identity
(ulq + allu.., n.) dx - 0,
j
vhere Yt is a smooth functionp finite in the regiou ;Aver consideration. The main
part of the argument consists in shoving that if a oolution u(x,~) of (7) Is
;defined in th6 cylinder Q2 -- K2 x CO.*a3 and if Its range is then
Osc (a. QJ < q O-'x (U. QJ
Cl X 5/4a, aj K jjxj ~6 1 Then the full
"ere Ql is the cylinder I
statement Ltoo long to be repeated he~ej oi the result for Ig-eneralized) solutions,
of (3) is given, followed by an outline of the method to be used in the case of
0 equations (5) and (6).. Orig. art. has: 16 equations.
ASSOCLAMON: Lieningradekoye otdeleale Matematicheskogo instituts, ime V. A.
Steklova Akademii nauk SSSR (Leningrad Division of the Mathematics Institute.
Academy of Sciences,, SSSR)
SUBMI l8Dec63 ="L: 00
Card 3/4

ACCWMON NR: AP4034025
OTM: 001
'SUB CODE: MA NO FEF SOV. 001
Card
4/4

AP40.

ce,
~64
Mathe
do,

-011ga I'deksandroma; UPA]11~.TWA, Nina Nlikolayevna;
SOLCI-VK) M.Z., red.
[Linear and quasilinear elliptic equations] lineir-ye i kva-
zilineinye uravneniia ellipticheskogo tipa. Moskva, Nauka,
1964. 538 p. (MIRA .18:1)

LA.DYZHENSKkYkp O.A.
In memory of Vladimir Ardmevich Steklar, 1864-1926 --n ths
100th anrdver.-ary of his birth. Trudy Mat. inst. 730-4 164.
(W-'RA IS
:3)

SOLONNIKOV, V.A.; PETROVSKIY, I.G., akadendk, otv. red,; NIKOI,ISKIY,,
S.M., prof., zamestitell otv. red.; LADYZHENSKAYA O.A., red.
(Boundary value problems for linear parobolic systems of
differential equations of the general type.) 0 Kraevykh
zadachak), dlia lineinykh parabolicheskikh sistem differentsiall-
nykh uravnendi obshchego vida. Moskva, Naukka, 1965. 162 p.
(Akademdia nauk SSSR. Matematicheskii institut. Trudy, vol.83)
(MIRA 18,-11)

LAJ)YZH-*,'IiSKAYA. O.A.; STU-rYALIS, L.
Mixed type equations. Vest. ILU 20 no.19:38-46 165- (MT HA 18:10)

.TOPIC TAGS: numerical analysis Navier Stokes equation, numerical
solution .tinite. dIfference. scheme
..'Two new convergent finite-difference schemes are proposed
the three-dimensional boundary-valu6 problem for the syst
1/2 UDC:_ 517,90.8

____ SOUR-CE CODE- _j/66/092/000/0093/0099
ACC NR; AT7006687 b~/251
AUTHORS: Kzhivitskiy, A.; Ladyzhenskaya, 0. A.
ORG: none
TITLE: The method of nets for nonstationary Navier-Stokes equations
SOURCE: AN SSSR. Matematicheskiy inBtitut. Trudy, v. 92, 1966. Krayevyyc zadachi
matematicheskoy fiziki (Boundary value problems of mathematical physics), no. 4, 93-99:
TOPIC TAGS: Navier Stokes equation, sequencet convergent sequence, vector,
Euclidean space, boundary value problew
ABSTRACT: An implicit difference scheme for solving the general nonlinear, non-
stationary problem
~-rk
divu=O,
is proposed. Its convergence is investigated. The case of a bounded domain.Q and
a homogeneous condition is examined. It is shown that the system
Card

ACC NRt
AT7006687
-0
-0. +k
U? Vul -4--T ui.,t-~-fukul =-PAZI-i- I.
It- AXOk A A Azt A,
Uk =0, (2)
U", 18A.= 0'.
UAi It-0
and
k= (3)
is uniquely solvable in every layer for uh, ph for any fh, ah' It is also sho-.m that
from the set of solutions K~ constructed according to (2), a sequence can be
extracted that converges (when &t = ch -jO) on a weak solution (in the sense of Hopf);
of this problem. In the case of n - 2, the entire sequence converges on this solu-
tion. Orig. art. has: 16 formulas.
SUB CODE: 12/ SUBM DOE: none/ OITZIG REP: 0061 OTH REP': 001
Card 2/2

LADYMEMSKAYA, 0. 1.
Ladyzhenskaya, 0. 1. and Dudina, D. G. "On the signifincance of the 14aksim,)v reaction
under conditions of the operation of the Ivenotryads'", Voprosy
dermato-venerologii~ i0l. IV$ 1943, P. 310-11.
SO: U-373619 21 May 53, (Letopis 'Zhurnal Inykh Statey, No. 18, 1949).

LADYMSIMAYA, 0. 1.
Drozdov, 14. F. and Ladyzhenskz I., and Luzina, V. N. "The cytological picture of
.~Za, 0. t.
itrethral pus and morpMo6gical changes in NdiSBer's gonococcus in
penicillin therapy," Voprosy (lemato-venerologii., Vol. IV, 13143, p. 1--A17-20.
SO: U-3736, 21 may 53, (Letopis 'Zh,Lrnal Inykh Statey, No. 18, 1949).

Y;~ 1v ,-- /V
LADYZHENSKIY,.A.
Movable platform for laying cables. Mast. ugl. 6 n0-7:12 JI 157.
(MTRA 10:9)
1 Pomoshchnik glavnogo makhanika shakhty "RudnichnayaO kombinata
M;1otovUgol'.
(Coal mines and mining--Equipment and supplies)

LADYZ KIY A. -
WO;
Attention designers* Mast. ugl, 7 no. 6:30 Je '58. (MM 11:7)
1. Shmkhts "Rudnichnaya" trests Kizalugoll
(Hine hoisting)

LADYZHF,BSKIY, A.
Cutting out rubber packingso' Mast. ugl. 7 no. 7:20 J1 158.
(141RA 11:6)
1. Pomoshchnik glavnoge fftkhanika shakhty *Rudnichnaya" tresta
Kj:ze lugol I
iCoal mines and mining-Squipment and supplies)
(Packings(Machanical engineering))

LAMMMMY. A., pomoshchnik glavnege makhanika
Numk-%~4
Shock absorber for conveying machinery. Mast. ugl. 7 n#.32:21 N 158.
(KM 3.1:12)
l.Sbakhta "Rudnichnaya" tresta Xizelugoll.
(Conveying mchinery)

LADTZH3MSKIT, A,
=biere is a need for directives on the preparation of tochnical.
ndustrial, and financial plans. Prom. koop. 12 no.10:10
Indust
I
0 158. (?CRA 11:10)
1. Nachallnik planavo-ekonomicheekogo otdola oblpromsoveta, Voronezh.
(Industrial management)

LADYZHENSKIY A.B.
Aggravation of latent tuberculosis in adolescents. Probl.tub.
no.6:42-47 161. (MMA 14:9)
1. Glavnyy vrach Cdesskoy detskoy tuberlculeznoy bollnitsy.
(TUBERCUIJDSIS)

1. LADYZHT~SKIY, A. M. - DU.RDE-D;F,,VSKIY, V. N.
2. ussR (6oo)
4. Bacterial Warfare
7. The use of bacteriological weapons is a crime against international law.
Vest.Mosk.un. 7 no. 11, 1952
9. Monthly List of Russian AcCeBSions, Library of Congress, March 1953, Unclassified.

lei
Eli
a SA, r r
pap
lot ii H ~ 1i ,
L4
F I .;.I, R
A
IF A. 2 P, :L
P!, Ts~
F.
IR
IF
41
Ps, 4t; n 12
fir
Pei '98.
I

liquid Ur "I I. t7lt I 14h
1144).-Two JeerlholP U iWO M5 "Nif 1hiskidAwli 4d A"I
irtr tcitcd. lei the lut. aftecr tile bluw. I ~1-. u1 Np`i,
in slid 0.81 of 45" FrSi wt-rc euld,,d, and i.
v -11 "ll"ilivil fill lwttct mi,eing. 11w A-49 wm three
olial."ll by Addli. Of -41111 All') 1114' -I&VI IIAIIJCIMI 111141
611" Shm it Wal fitledlY dro,i6liml vvith U-V' tel Al.
hC L V11. afire Ilk' 11141W. J',, 44 volu'l.1
!11 1 'tell pI`(X
level u.131!lextred slowly 111to tim tvnvcglt,r at I~MA:Qj
Ittic trto . uf lite 4xitimtri mcrl wAs HM 401 ovi Ill,
WA4 41LAILVOI. 111V lr.M 6011 W;4% *1 litlit VM11A W
cladusel1v -smoril Alfrv 31 uOrt. -4
'16% VC1111 was added, the gag thickerknd %ilb %asset and
,be ACT) transferred ilito Iscilre; where it wab raltally de.
"Iddil"t with (1.24'; of 46c0 VvSi tiled ill & few j.nsm ullh
At.
"he tell 44 lf'"r d"111(lati(Ill fill'th(kU Irdim-d Ifir
11,,t~tlt in if,,- txan-riter ocri ley jsjiA2e;. ,,let Ilk.
y 1611 of the latter (or mmv-, %W1 r-k.-I
ly C in the Pig iron. in the fil"t steel dcosidi" by the
red 'be () "a" ter O-feel-ir* IOWer thAill ill thr %t,,.l
dowitidirril by tile Ist Ineflu.j. " N1. It-h

01
It*
E-4
a~
-Doe 48
a4 Steel, Bessemer
Metallurgy, Ferrous
Oftelindnary Deoxidation of Steel Made by the Short
Be"emer Process With Molten Cupola Pig," B. X.
1&Cqzb--nskiy. Cand, Tech Sci, VIMOM and VNITOL,
6 pp.
VU1 I" 11o 12
Pa4wents results of a comparative study of two
Imthods for deoxidizing Bessemer steel: (1) using
7% ferrcuanganese (1.3%), 45% ferrosilicon (0.8%),
and, aluminum (0. 1%), and (2) using molten cupola
VIS iron (30, 75% ferromangawGO (0.8%), and 45%
18/49TS9
UWE/Metals (Contd) Doc 48'
ferrosilicon (0.2%). concludes method (2)
Is feasible. It saves 12 kg fa=ooilicon and
i 10 Xg fOrrOmangenese Per ton of usable steel.
4~
I A9W9

USM/Metals - Steelmaking Xar 51
"Intensification of the Steelmaking jProcess in
Aide !.Blown Converter, " B. N. Ladyz,'henskiy,
bond Tech Sci, Altaysellmash
"Zoltey Proizvod" No 3Y PP 5-8
Xaptl beets were conducted to study effect of
ore addni on the bloving period and on, decrease
luconsumpti6u of ferrosilicon. Keebarism of
O~ddation of Mn, Si and C is,similar to that of
8"el-manufg process: in ope-u~-hearth or elec fur-~
4*6es, i.e., atm oxygen ls.trans~erred Into meta3
195T50'
OW/Metals Steelmaking (Coutd) Mar $1,
mainly through ferrous oxide. A'4du of ore, it-;
Masing the content of ferrous oxide in slag)
luareases the oxidation rate and shortens theL
time required for bloving the melt.

LiDYZHBNSKIT, R.N.; ORMKIS, V.D., kandidat takhnicheskikh nauk;
I XI llm!T IN.S.; I)OIROTVORSKIT, M.M., professor, rateenzent;
BCMNCIV. K.A.. dotsent, retsenzent, TARWOV, N.P., tai*a-
cheuki7 rodaktor.
[Youndinid Liteinos proizvodetvo. Pod red. V.D.Oreshkina.
Moskva, Goo, nauchno-tekhn. izd-vo mashinostroit. i sudoetroit.
lit-r.r, 1953. 207 P. (MLRA 7:8)
(Pounding)

Stec -e-
rt
prW.er.s of sTne3.tinc, stec3- -L,
~ of Russian Aceessir-)II-:1 Lilcrar7 Of ConCress
l4onthl"', List
!;~~ lLrjlK,L-
june 1953.

JDnMSKIT*v nank; TWOT, V.P., laureat
kandLidat tekhnicheeldkh
M ,,
premii, inthener; BWMTA, P.N., doIrtor takhnichaskikh
nauk, professor, retsenzent; IONOPASEVICHO V.A., Inzhener, redaktor;
MCESLI, B.I., tekhnicheekiy redaktor
(Smelting steel for mold casting] Vyplavka stali dlia fasonnogo
litlia, Moskva, Goo. nauchno-tekhn. Isd-vo mashincetroit. lit-ry,
19%. 382 p. (MLRA 7:10)
(Steel castings)
(Smelting)

IVANOV, V.G., kandidat tekhnichaskikh nauk; KRTANIN, I.R., kandidat tekhniche-
skikh nank; IAXSHMKIT B I -bundidat tekhnichookikh nauk.
au":Z~
Overheating of low Bessemer steel. Lit.proisv. no.4:31-32 Ap '56.
(Bessemer -process) OMn 9: 7)

IADTZH3MKIT, B.N., in2b.
Using low-frequency crucible furnaces. Hashinostroitall no.l:
45-46 N '56. (KIRA 12:1)
(Smelting furnaces)

L A-_V V -L tt-E-14" 5 K fV ( K 0 L. "k- 1 ~_4 i C t+
PHASE I BOOK EXPLOITATION 475
Ladyzhenskiy, Boris Nikolayevich and Tunkov, Vladimir Pavlovich
Tekhnologiya izgotovleniya stallnykh otlivok (Technology of Making
Steel Castings) Moscow, Mashgiz, 19571. 255 P. 7,000 copies
printed.
Reviewers: Zverev, K.M., Engineer,, and Kreshchanovskiy, N.B.,
Candidate of Technical Sciences; Ed.: Talanov, P.I., Prof.;
Ed. of Publishing House: Sirotin, A.I., Engineer; Tech.td.-.
ElIkind, V.D.
PURPOSE: This book was written for engineers and technicians In
foundry shops and for engineers and designers in the machine-
building industry. It may be used as a manual by students
studying casting methods.
COVERAGE: The author attempts in this book to discuss the main
problems of the casting of various parts for the machine-building
industry. These problems, including some theoretical considera-
tions, are reviewed in sequence starting with part design, mold
Card 1/5

,Technology of Making Steel Castings 475
and pattern making, casting, thermal treatment and the repair of
fl*ws in the cast parts. These methods are said to be the most
advanced ones and are believed to represent the recent achieve-
ments of Soviet scientists and engineers, and the present trend
in the Soviet industry. Personalities mentioned are L.N., Podvayddp,
who wrote chapter VI, and K.P. Baryshnikov who assisted the autbpv
in writing chapter VII. There are 71 Soviet references.
T"I OF
CONftNTS:
Introduction
3
Cl~. I. Fundamentals of Steel Casting Design 5
1. General information 5
2. Technological design considerations 9
3. Structural design features 11
Ch. II. Design of Castings
1. General information
2. L*eation of part in the mold
26
26
26
Card 2/6

Technology of Making Steel Castings 475
3. Determination of parting line 27
4. Selection of mold preparation methods 28
5. Selection of molding method 28
6. Blue print for casting 29
Ch. III. Fundamentals of Mold Design Technology 37
1. The mold and molding material 37
2. Cores 50
3. Gating 59
4. Risers 72
5. Cooling and insulating materials 103
Ch. IV. Baking of Molds and Cores 114
1. Basic facts about baking of molds and cores 114
2. Methods of baking molds and cores 117
3. Baking conditions for molds and cores 120
Ch. V. Filling of Mold and Cooling of the Casting 126
1. Temperature of poured metal 126
~. Holding the casting in the mold 128
Card 3/5

Technology of Making Steel Castings
415
Ch. VI. Thermal Treatm 'ent of Castings 136
1. Various methods of thermal treatment 136
2. Internal stresses and methods of thermal treatment 140
3. Thermal treatment of carbon steel castings 142
4. Thermal treatment of alloyed steel castings 146
5. Quality control of thermal treatment of castings 152
Ch. VII. Steel Casting Practice 156
1. Bottom-poured stacked mold casting
2. Manufacture of thin walled castings 161
3. Casting of parts for agricultural machinery 168
4. Casting of fittings 171
5. Casting of parts for tractors 176
6. Casting of parts for transportation machinery 179
7. Castings for heavy machinery 187
8. Casting of forging dies 202
9. Casting of reinforced catings 206
10. Casting of crank shafts 209
Ch. VIII. Special Features of Alloyed Steel Casting 211
1. General information 211
2. Technological and structural considerations in design
of castings and in mold making 213
Card 4/5

Technology of Making Steel Castings 475
3. Defects common to steel alloy castings 216
4. Surface alloying of castings 217
Ch. IV. Defects in Castings, Detection and Repair 219
1. Defects In castings 219
2. Detection of defects 234
3. Eliminating defects 240
Bibliography
AVAILABLE: Library of Congress
252
Card 5/5 GO/ad
8-26-58

~.,-Mtii ~A.We

195L

-7-7777--

IADYZHRNSKIY, Boris Ni~91A vleh-
, _ _Xv TUNKOV, Vladimir Pavlovich; ZVXW, X.m.,
6 ;;~. nil : KOSHCHANOVSKIY. U.S., tand,tekbu.nauk, rateenze4t;
z rw"
TAIANOT, P.I.. prof., red.; SROTIN, A.I., inzh., red.izd-va;
ILIKIWO T.D., tekha.red,
[Technology of preparing steel castings] Tekhnologiia i'zgotovleniia
stalinykh otlivok. Moskva, Goa. nauchno-tekhu. izd-vo mashinostroit.
lit-ry, 1938. 255 P. (MIRA 11:4)
(Steel castings)

13 E N
PHASE I BOOK EXPLOITATION SOV/5411
Konferentsiya po fiziko-khimicheakim o9novam proizvodBtva stall. 5th,
Moscow, 1959.
Fiziko-khimicheskiye osnovy proizvodstva stall; trudy konferentsil.
(Physicochemical Bases of Steel Malting; Transactions of the
Fifth Conference on the Physlcchemical Bases of Steelmaki"I
Moscow, MetaUurgizdat, 1961. 512 p. Errata slip inserted.
3. 700 copies printed.
Sponsoring Agency: Akademiya nauk SSSR. Institut metallurgii imeni
A. A. Baykova.
Responsible Ed.: A. M. Samarin, Corresponding Member, Academy
of Sciences USSR; Ed. of Publishing House: Ya. D. Rozenteveyg.
Tech. Ed.: V. Mikhaylova.
Card 1/16

t
Physicochemical Bases of (Cont.) SOV/5411
PURPOSE: This collection of articles is intended for engineers and
technicians of metallurgical and machine -building plants, senior
students of schools of higher education, staff members of design
bureaus and planning institutes, and scientific research workers.
COVERAGE: The collection contains reports presented at the fifth
annual convention devoted to the review of the physicochemical bases
of the steelmaking process. These reports deal with problems of the
mechanism and kinetics of reactions taking place in the molten metal
in steelmaking furnacesi The following are also discussed: problems
involved in the production of alloyed steel, the structure of the ingot,
t-he mechanism of solidification, and the converter steelmaking
procavo. The articles *contain conclusions drawn from the results
of experimental studies, and are accompanied by references of which
most are Soviet.
Card-2118

Physicochemical Bases of (Cont.) SOV/5411
Ladyzhenski-y, B. N., and M. V. Karakula. Making Low-Carbon
j iRoyed_9fe_e_Ts =Acid Open-Hearth Furnaces 27
Stroganov, A. I., and A. N. Morozov. Behavior of Chromium in
the Bath of a Basic Open-Hearth Furnace 39
Petukhov, B. G. Making Chromium-Nickel Steels in Large Open-
Hearth Furnaces With the Use of Nickel Oxide' 46
Omarov, A. K., and A. Ye. Khlebnikov. Intensifying the Working
Period of the Open-Hearth Scrap Process 54
[ The 'f ollo*ing persons pai-ticipated in the research work:
Engineer Munasypova, Engineer T. Kovaleva, and Technicians
U. Rakhmanulov, V.V. Ponomareva, L. Rusnyak, Z. Zaporozhan,
A. Perkova, S. Bilyalova, and V. Guseva.]
Card 4/16

GCROZHAMR, A.N., kand.tekhn.nauk-, HOVITSEIY, V.K., 1mud.tekhn.nauk;
KMEN, I.R., dbktor tekhn-.iwuk; IODMVSKIT, S.A. i kand.tokhn.
nauk; LU=HENSXIY,_B,B., kand.tekhn.nauk; MILIMAX, B.S.j kandotekhn.
nauk; KIOCHM, R.I., kand.tekhn.nauk; TSYPIN, I.0-0, )=d.tekhn.
nauk; LEVIN, H.M., kand..tekhn.nauk; RUM, A,L., inzh,; LYASS,
A.M., kancl.tekhn,.uauk; GENUUAK, B.Z., kand.tekhn.nauk; ASTAFIYEV,
A.A., kand.tekhn.nauk; YEFWAKOV, k.A., inzh.; GRIBOYEDOV, Yu.N.,
kand.tekhn.nauk; HYASOY3DOV, A.R., insh.; BOGATYRE7, YU.M., kaud.
tekhn.nauk; UMMOV, Ye.ps', doktor.tekhn.nauk, prof.; SBDFMLN, L.A.,
Imnd.tekhn.nauk; PERLIN, P~I., iixzh.; MOSHNIN, ge.N., kand.tekhn.
nauk; PROZOROV, L.V.. daktor tekhn.nauk; CHERNOVA, Z.I., tekhn.
red.
-[sodg1U~AOgj.aiL__pidbl' i:113,,-~thamanitv~oture of h vymaohine
ry
tiazhelogo mashili6stroeniia, Mftkva,
Goo. nau6huo-t ekhu._izd.;.vo--u'ash1nostro1 t. lit-ry. yhet!TiOteel smelt-
i treatmentj me
tale ~y prep!'.
'ra _-Y ta1hoe_proiivoletp
e lavlm 1 r0, t;b1rmjAb_
kaia' obraboticiL','--obrabot)mlMa-11~v davleniem., 19
60. 26~ P. (Moicow.
?Sentraltnyl nauchn6.4isledovatellakii Institut tekhnologii i mashi-
n6stroenita. fTrudy] uo. 98). (MI]RA 13:7)
(Steel) (Youndirg) (Forging )

I , Burts Nikolayeviolq- BAMMAKOV, Aleksamel Dmitriyevich;
POZDNYAKOVA2 G.L.., red. izd-va; VMqETSKIY, S.I.., red. izd-va;
OBUKHOVSMA, G.P.., tekbn.-red.
(Treatment of liquid metals by powder in a gas stream] Obrabotka
zbidkogo metalls, porosbkami v strue gaza. Moskva., Goo. naucbno-
tekbn. izd-vo lit-ry po chernoi i tsvetnoi meta3lurgii., 1961* 115 P,
(MIM 14:12)
(Powder metallurgy) (Liquid metals)

211~2
133/61/000/001/003/016
AO54/A033
AUTHORS: jLadyzhens~iy, B.N., Candidate of Technical Sciences; Bashmakov, A.D.
Engineer
TITLE: The Dependence of Metal-Desulfurization on the Conditions of Mass
Transfer
PERIODICALt'Stal', 1961, No. 1, PP. 29 - 30
TEXI!: At steel melting temperatures chemical reactions take place at high
velocities. The only factor limiting the reaction speed is the mass transfer at
the place of' reaction depending - among other things - on the temperature condi-
tions, the diffusion of the reacting substances, the size of surface on which the
reactions take place and on the layer thickness. Evidently, by Improving these
conditions, several metallurgical processes could be accelerated. Based on the
above considerations and tests, satisfactory results have been obtained by using
powdery matarials during the melting in hearth-type furnaces, for the purpose of
accelerating the desulfurization of the metal which, under normal conditions, is
extremely sLow (0.00007 - 0.00125% S/min). This is mainly due to the small reac-
tion area between the metal and the slag relative to the weight unit of the metal
Card 1,6

22572
31133161100D100110031016
A054/AO33
The Dependence of Metal-Desulfurization on the Conditions of Mass Transfer
(S/T), for which the following values have been established:
Furnace S s T, m2/t
15-ton open-hearth furnace ........... ........ 0o9
125-ton open-hearth furnace , ........ 0.4
arc furnace .... 9. .......................... ....,,-M
induction furnace .... *.......................... -4.2
An increase in this specific contact surface not only enlarges the reaction area
but ali6 increases the thickness of the layers taking part in the reaction which
also contributes to accelerating the mass transfer at the place of reaction.
Blowing powdery materials, f-Inely crushed slag-.forming substances by a gas jet irr-
to the liquid metal in the. ladle, the de sul furl zstion speed of the metal increased
to 0.005% S/min (Ref. 1, B. Ladyzhenskiy and N. Sashchikhin, ITEIN, No. 743, 196D).
By blowing powdery fluxing agents with a specific surface of 435 cm2/100 9 into
the metal In amounts of 5% of the weight of the m6tal to be blown through, there-
action area can be enlarged to 200 m2/41-on and the desulfurization rate can be
raised to 0.2% S/min. The effect of the reaction surface of the phases on thede-
sulfurization rate is verified by an analysis of the equilibrium condition of Sul-
fur In the metal-slag system (Ref. 2, Fischer and Spitzer, Archiv f. d. Eisenhft-
Card 2/6

22572
S/133/61/000/001/003/Oi6
A054/AO33
Thd Dependence of Metal-Desulfurization on t-%.e Conditi:ons of Mass Transfer
tenwesen,, 1958,-No. 9) (Fig. O-J. for the conventional desulfurization process and
'also for; the new method, using pulverous substances. -In the first case the m~tAl
was melted in a 12-kg lime-dolomite crucible of aft induction furnace, containing
0-030% S.. After adding lime it was held under slag at 1,6000C for two hours. In
the second case the metal was melted in a 5049 magnesite crucible of the induc-
tion furnace, heated up to 47000C, blown through with a mixture of 55% CaO, 4VO
CaC2 and 5% Al. The'quantity of mixture employed amounted to 4.5 % of the metal
weight with a temperature drop of 2000C during the blowing process. Nitrogen was
used as carrier gas. Figure 1 shows that the-S-equilibrium in.the'netal-slag sys-
tem is-attained in 50 - 60 min in the conventional process, whereas in the new
process it takds on* 2-5 min to reach'this point. Another feature of mass trars-
fer influence on d41fur-17-shy on is the fact that slag and slag-forming substances,
are more fully utilTed in separating sulfur from the metal. In Figure 2 compar-
ison is made on the elationship between the distribution coefficient of sulfur
'By enlarging the sppcifi0
in the metal-slag syptem and the basicity of the slag.
contact area betwee *metal and flag, the amount of sulfur separated from.the met-
al increas
-es, the b icity of the slag remaining the same. The minimum degree of
sulfur removal in tl open-hearth process-corresponds to an S/T value between 0.4:
Card 3/6

22572
S`/133/6i/ooo/ooi/oo3/oI6;

A
054/A033
The Dependence of Metal-Desulfurization on the Conditions of Mass Transfer
0.0 m2/ton, while-the maximum is attained in'the process of blowing through the
crushed powdery mixtures,
metal finely for which SIT exceeds 200 m2/ton. There
.
are 2 figures and 2 references; 1 So-
v.iet and.1 Non-Soviet.

ASSOCIATIONi TsNIITMASh. S

Figurei 1: Establishing the sqlfur
equilibrium in the metal-s 'lag system C
with various methods of desulfuriza- 4-1'
tion. a - holding the metal under
0
lime slag (Ref. 2); b -'blowing pow- 43
o'
dery mixtures, in a nitr
ogen gas 0
01
current, into the metal. S

W X VY It/ al X/
card V 6 time, min

VLASOV, V.I.; KOMOLOVA. Ye.F.; LADYZHENSKIY B N kand. tekhn.
0 * -- -y-
nauk retsenzent; MOWN, u.L.,, inzh., red.izd-va;
SMIRNOVA, G.V., tekhn. red.
(Cast G13L high-4hganese steel; properties and manufao-
turel Litaia vysokomargantsovistaia stall G13L; evoistva
I proizvodstvo. Moskva, Mashgiz, 1963. 194 P.
(MIRA 16:6)
(Manganese steel) (Steel castings)

ANIDALOV, M.P.; LADYZHENSKIY, B.N.
Organizing the operation of electric melting furnaces in mass
production foundries. Lit. proizv. no.10:11-22 0 '63. (NIRA 16:12)

REPA42-B.N.; KULINICH, V.P.; KATEYEV, Yu.V.; ZARUBIN, S.N.; ROZENBLIT,
Ya.L.; ABROSIMOVY V.I.
Desulfuration of acid electric steel by tho'bloving-in of powderlike
limestone. Lit. proizv. no.8:42-1+3 Ag 164. (MIRA 18:10)

B.,q., kand f-r-.,khn. rAifK; YrzhtV, G.r
s0rap metial in the qi&s-bl_OwD Oxygen ccavertmr process,
gc'"Orlld- P:'Om. n,-)*6,.-21-23 N-D 165. (MIRA IS.-12i

YAKOVLEV, Nikolay Nikolayevich; GLUSHCHENKO, Viktor Grigorlyevich;
LADYZHENSKIYp B.R.j retBenzent
[Steel production in small converters] Proizvodstvo stali
v malykh koirverterakh. Moskvap Metallurgiia, 1965. 142 p.
(MIRA 18:7)

1ADYZIMSKIY, 3. V. and TUIZOV, V. P.
IISteel Smelting for Shaped Casting," Sci. and Tech. State Publ. House .4;."or Liter-
ature on Yachine Construction, Moscow, 1954
Trarslation of Table of Contents and summary of context - D 257848) 6 jui- 55

LA!HZHENSKIY G.N. [Ladyz hens lkyi, N.Mj. KIRICHENKO, 1.11. [Fyrychenk&, I.P.1
- . - .1.. ... 7. - - - i i
Mineral composition, minor elements, and the ati-acVure of 'the
Upper Cretaceous and Faleogene sheLls and skeletons of marine
organisms in Bakhbhisaray District of Crimea Province. Dop. AN
URSR no.7:907-910 165. (MIRA 18.8)
1. Llvovskiy gosuclarstvennyy universitet.

Conditions for total continuity of P-8-Urysohn's operator valid
in the space L-P. Trudy Mook.mt.ob-va 3:307-320 154. (KLHA 7:7)
(Operators (Mathematics)) (Spaces, Generalixed)

XRLSITOSILISKIY, N.A.; LADYZHIESKIY, L.A.
Structure of the spectrum of positive heterogeneous operators.
Trudy Koek.z&%.ob-v% 3:321-346 154. (KLR& 7:7)
(Operators (Mathematics) (Topology)

JOBJECT USSRZMATHEMATICS/Funotional analysis CARD 1/2 PG - 744
AUTHOR LLDYZENSKIJ L,A.
TITLE On non-linear equations with positive non-linearities.
PERIODICAL Uspechi mat.Nauk 12, 1, 211-212 (1957)
reviewed 5/1957
The author investigates the positive solutions of the equations
(1) -A A
and
(2) ?kL (f + f
in a Bartach space with a cone, where A is a non-linear operator and AG - 0.
It is assumed that A has the following propertys In the cone K there exists
an element u such that for every
u0 ~> A 9u0
(,A- r( f) and V _V are positive numbers) and for every -f >/ Y'Uo > 0)
and arbitrary nil-bers a and b (O< a (1 + -1) tA If 9(a 4t 4,b), I - I (ab, %P) >O.
Under this and some further less essential conditions it is shown 1) that for

Uspeahi mat.Hauk 12, 1, 2*11-212 (1957) CARD 2/2 PG - 744
A 6 ( /N09 NCO ) there exist positive solutions of (1) and for AE ( Xo,+T,)
there exist positive 3olutions of (2) and that they are unique; 2) that for
other ~L-values (1) and (2), respectively, have no positive solution being
different from zero; 3) that the positive solutions of (i) and (2) depend
continuously on-?~ and they increase monotonely with)~ . Besides a method
for the determination of ';k0and -A CO is given.
A detailed representation of these and similar results is contained in the
author's thesis (Kasanj, 1954).

16(1) 05256
AUTHORS: Krasnosellskiy,M.A., and Ladyzhenski:r,L.A. SOV/140-59-5-12/25
TITLE: On the Extent of the Notion uo-Conca,re Operator
PERIODICAL: Izvestiya vvsshikh uchebnykh zavedeniy. Matematika, 1959,
Nr 5, pp 112-121 (US-OR)
ABSTRACT: The authors consider
M A f(x) = iG1XPyq'f(y J] dy
F
An operator A in the Banach space E which is partially ordered
with the aid of a cone K, is called u 0- concave if it is positive
and monotone and if there exists a positive element u0 so that:
1) For every tKX(V %PP / 0) there exist orep, so that
(2) ofuo4A\0j[uo (C.S-.0), and arbitrary O