SCIENTIFIC ABSTRACT BAKBARDIN, Y., V. - BARBYMV, I.

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• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R000103110002-3
• Release Decision: RIF
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• Document Page Count: 100
• Document Creation Date: November 2, 2016
• Document Release Date: June 6, 2000
• Sequence Number: 2
• Publication Date: December 31, 1967
• Content Type: SCIENCEAB

BAKSMIN, Yu.Y. (Kiyev)
-----------'--! `;~ !44
Trantme~n'~ of pricinry tumors of the Iris. Vent. oft. 71
n0.2- -46
(IRIS, neophame (MIRA 11:4)
ther. of Drimnry tunors)

BAKBARDIV, Yu. V.
Use of carbon dioxlde unov to form an adhesin
Inflamation of eyvs
tiasuose Oftozhur, 16 no.6%334-3)6 161. (KRA 14811)
lo Is kafedry oftallmologii (nachallnik - prof. B,L.
Polyak)
Voyenno-tieditainsko7 ordena Lenina akademii tueni
S.M. Kirmk.
(DRY IM- THERAPEUTIC USE) (RET.LNA--DISMES)
400,

.PAKBARDIN, Yu.V.,, poilm-ovnik med.sluzhby
Use of lytic mixtures in ophthalmic surgery.
Sborenauchetrude
Kiev,okrush.voonagospo no.4033-334 162. (MIRA 1615)
(ANESTHESIA) (EY&--SURGHRY)

'7- 7-r v . T- . , -1- . , t -i'VI --- , - . -, . ~ I
~ 1 -, T7-. - TI-IL - . V .1-
7aAK7AT ~ --, , I ". ~ . , F_~oTTT~1-11 p . I- 1 41 ,
-. . ; -
"On Eye Injuries".
Voyerno Wditsiziskly Murnal , No.4, 1~~'?

BAKBARD Yu (Kiyur)
-ftye
Lymphogranulomatosis wit inary localization in the
orbits.
Vrach. delo no.9t15O-l52%,ff63. (MIRA 16tlO)
Oman I DISEM) (ORBIT (EYE) - DISEAM)

tl
C.'. ry -ftsluzheraiyy

BAKBERGEN!C,V, S.
(Beacons; a collection of easpys about
heroes of the
seven-year plan) Painki; abornik ocherkov o
geroinkh
semiletki. Alma-Ata, Kazgoslitindat, 1962.
284 p.
(MIRA 16:11)
(Kazakhstan--Economic conditions)

SARDI, Gyorgy, okleveles gepeotmrnok*; DAKCSI,
Robert, okleveles
gopeszmernok -
Air injection channels of passenger "cea in
motor tred no.
Epulotgapeezet 12 no.5.-161-164' 0 163.
1. Gans-HAVAO Vagonazerkeettes.

I loq gqpf) r. I, rm, r n:A ; ~',-V',: tliyurgl , 01, 1)
v" 10 A RO Pasznhirnok
BAK!,
A'.r dnoto of ro-om )f n rmil litno 90p
no.4sl2l,126 Ap 165.

i Irw!% Ivy 1,0 P IV--,I 1)05157;~IXW F4 1
I r
tire unifutrinly boup(INI: bf
~jj-j w,f a trimutuLtz !un 7' tJ 1)
'i P. P'll ,:11) -11111- ",W)"i
A VrvA
t 41 it I Ayf oi-is in 1!1(! 1.1 col 11fin C of
thel, T i, -~IiJ U,, h-1w: 1--1204,41
Vol 1~0. lo;

;y -. ~',
- -, 1~-, i L-1
Dissertation: 11.3riooth Sur.'aco.-, WiUi Gonoralized Socojyl
Derivativ;:s." Jand Phys-:-~ath Scip
Leningrad State 11j, Lonirk:rad, 1954. Reforati-nVj
Zhw,nal---'-'atcmaUka, :.:o.-,cow, Jul 54-
SO: SLP,-: No. 356, 25 Jan 19~5

41keYm-&-n, 1. Ya.-, D-Air-min a tio'n, o- I a- s'urfs c'e -k-Y,
wond quadratic lonaL L'Bpehi
hbt~ Nauk (NS-) 9, no. 4(0), 155-161 (tq,;4), (Rus-
.iaO I J1/ W
Let D be a domain in a (ti, v)-plane bouneed by a simple
clockA tvlygon. Conskirr the clam 11' of all Stirf3m.; in F1
gk-cn by position vectors r(m. Y) defined nP. vhco~ r(u, v)
is of cta-,-- C1. jr.Xr,j >0, and all rencra6cd Ewromf patual
drri-;ativei of r(u, r) in the mose of Sobolev cxist. Lrt E, F,
G. 11. Af, N 1w defined in the msbal way, uhvv,~, tar instance,
r., in L ~- Jr._ r., tj stwnds for a gcncralim] de'rivalive. If
for tm, mitfoc-ts in It' a ovic-to-4nnc cortc-INmOcrive betwecl)
thrir poln,s exists soch that the valkirs of E, P,G. I, Al, N
at corretpowNiq pAnt-; art! c(Iii.0 alintist rVerv%vile're in 1).
thtn the two wirfacusate ccmgr,*jvnt as 4~ts iii

BAULIKAM. I.Ya.
Plans surfaces with Generalized second derivatives.
Dokl.AN
SSSR 94 no.4:605-608 7 154. (XLRA 7:2)
1. Leningradskiy takhnoloegichaskiy institut im.
Y.H.Holotova.
(Surfaces)

I I I C-nij Nr. AF
T- -; b - T - -. -- - - -
I I I Moscow, Jun-Jul '50,
Transactiong c,f the Third All-union M&UICIMtical
Congre.3s)
Trudy '56, V. 1, Sect. Rpts., lzdatel'stvo AN SSSR.,
Moscow, 1956, 237 pp.
Bakellman, 1. Ya. (Leningrad) EvalUation Deformation
'-O?-a-C6jj;ie-x "ur ace. 136

BAXILIKAN. 1.T&.; TXR M , A.L.
Generalized derivatives of continuous functions with
two variables.
Ump.matonank 11 nool;17)-179 -Ta-F 156. WaA 9:6)
(Funations, Continuous)
1.

~F-, T-
SUBJECT USSR/MATHEIUTICS/Goometry CARD 112 Pq - 468
1UTHOR BMLIKLN I.Ja.
TITLE Differential geometry of smooth irre lar surfaces.
PERIODICAL Uspechi nat,.Nauk j_tL 21 67-124 (1956r
reviewed 12/1956
The author shows that moot of the results of the classical
differential
geometry can be transferred to surfaces which are described by
functions
which possess continuous first derivatives and second
derivatives ganeralized
in the sense of Sobolev. Here it is assumeA that the latter
ones in the
considered regions of surfaces are summable with square. The
author asserts
that these irregular surfaces, according to their inner
geometry, belong
to the class of two-dimensional manifolds of bounded curvature
due to 11exan-
drov.
Thepaper containti a connected representation of the
differential geometry
of the mentioned surfaces. The first ohapter brings definitions
and proper-
ties of generalived derivatives of vector functions as well as
necessary ard
sufficient conditions therefore that a smooth surface z -
f(x,y) possesses
quadratically sunmable generalized second derivatives inside of
a square D.
In the second chapter inner-geometric properties of the
surfaces are treated.
It is asserted that the metric of the considered surfaces
possesses a bounded
curvature and that to the notions of the innjr curvature and
the variation
(according to Aloxandrov) in this came there corresponds the
integral of

Uapechi mat. Nauk 11, 21 67-124 (1956) CARD 2/2 PO - 466
Gaussian curvature with respect to the area and the integral
of the
curvature with respect to the arc length. The third chapter
brings
connection betwedn the inner metric of the surface and its
form in
space. Poterson-Xodazzils formulas and the theorem of GauB
on the equality
of the area of the spherical image and the inner curvature
are generalized*
Criteria are given for the sign of the curvature of the
inner metric.
shown that the oonpidered surfaces are determined uniquely
by their
and generalized second quadratic forma,
geodesic
the
the
It is
first

I _~ -.), 1~ -7
LTTT~
SUBJECT USSR/"- MERATICS/Goome try CLRD 1/1 rG - 339
AUTHOR BAKELMLNN I.Ja.
TITLE The estimation of the daformations of regular convex surfaces
in dependence of the -i'-%njge of their inner metric,
PERIODICAL Doklady kkad. Nauk 12L~, 358-361 (1956)
reviewed 10/1956
Let ~. and be regular closed convex surfaces with essentially
positive
Gaussian curvature. Let consist between the points k and a
one-to-one
correspondence, where in corresponding points the fundamental
terms of first
order and their first and second derivatives for botL surfaces
diffar little
from sachother. What then can be said about the deviation of th6ir
derivatives ?
This question is answered by the author by two tbeorems, one of
which treate
the closed surfaces and the other treats surfaces with boundae In
both cases
from the in a certain sense small deviation of the fundamental
terms and the
Gaussian curvature a small deviation of the position vectors and
of the
spherical coordinates (in the case of a closed surface)
respectively, is
obtained. The proofs base on properties of the solutions of
non-linear elliptic
differential aquations. I former result of Schauder (Math.Ann.
106,_ 661 (1932))
is used for somewhat weakened assumptions.
INSTITUTIONs Educational Institute, Leninggrad.

SUBJECT USSR/MATHMUTICS/Goome t ry CARD 112 PO - 729
WTHOR BL"'Llw.
IfTLE'' Differential geometry of smooth manifolds,
ARIODICAL Usptchi mat.Nauk 12.. 1. 145-146 (1957)
reviewed 5/1957
A surface is cillod smooth if in the neighborhood of each of its
points it
permits the parameter representation Zr - Z(u,v), whore ~.Y
(u,v) Is continuous-
ly differentiable and I Vyu ~(O_, 1 / 0. The aut)ior considers
the question of
the imbedding of smooth surfaces into the euclidean space. It is
assumed that
0- (u,v) beside of the mentioned properties has generalized
second derivatives
in the sense of Sobolev which in the neighborhood of each point
are summable'
in the square. This enables the author to introduce a second
generalized
differential form accordirW. to the model of the classical
difforontial
geometry, In certain points this may not exist and its
coefficients may be
disoontAnuoua and become Infinitely large., All fundamental
properties of the
regular surfaces can be transferred to the considered irregular
surfaces.
Lost of the relations appear only by replacing tY.* usual
derivatives by the
gentral.i2ed on*R.
Prom the point of view of the inner metric the considered
surfaces are
manifolds of bounded curvature in the sense of Alexandrow.
Almost all
coordinato lines possess a bounded integral curvature in the
space, consequent-
ly an integral goodiosio ClArvatur* for wnich the formulan of
the classical

Uspechi mat Nauk 1-2, 1~ 145 146 (1957) CARD 2/2 FG - 729
1
differential geometry are valld '.f the ordinary
derivatives are replaced
by generalized ones. The consil*ied surfaces admit an
approximation by
regular surfaces, where the inner metric of the
approximating surfaces
converges uniformly to the inner motric of the
approximated warfal-e.

20-114-6-1/54
AUT1IOR- Bakollman, 1. Ya.
TITLEi A Generalization of the Solution of the Monge-Ampdre
Equations
'Obobahchennyye rocheniya uravneniy Monzha-Ampera)
PERIODICALi Doklady Akademil Nauk SSSR,1957,Vol-114,Nr
6,PP.1143-1145(,USSR)
ABSTRACTs The author examines the Monge-Ampe're equation
rt - s2 w Vx,y) R(PW within a certain convex domain D on
the area (X,Y). ?(x,7 > 0 and R( -,q) >,, It a const ;;~ 0 are
here constant functions, the formed withinothe closed domain
D and the latter on the p,q - plain. As Zeneralized solution
of the Mon,-e-Ampdre equation the author denig-nates a func-
tion z(X,Y) which define!3 the convex avrface f for which on
any inner subdomain M of D the equation
- ff 9, (x,y)dxdy - f f d d cill(M) ls satisfied. The
M V010
Card 112 problem of the determination of the convex surface
with the

20-114-6-1/54
A Gcncraalization of the Solution of the Monge-Armpdre
Equ,-.:tiona
assumed R-plain of the normal j;raph is beat treatod by im-
posin,~ a limiting condition to the surface. The present
parer examines two types of such limitint; conditions. First
infinite convex surfaces are investignted. Then the Dirichlet
proble:a is formulated in the generalized rerrosentation. The
here obtainGJ theorems can be applied to functions of n
variables (n * 2).
Altogethor 7 theorems are given. There are 2 references, 2
of which are Slavi,.-.
ASSOCIATIONs Leningrad Pedagogil.,al Institute imeni A. I.
Gertsen
(Leningradskiy pedaf;ogicheskiy institut im. I. Gertsena)
PRESENTEM December 10, 1956, by V. I. Snirnov, Membor.of the
Acade..iy
SUTIMIT""M December 6, 1956
Card 2/2

AUTHOR: BAKELIMAN I. Ya. 20-5-1/1Z
WIT Apriori-Eatimations F%nd RoAularity of the Generalized
Solutiorw
of the Equations of May)~~,-Ampere (Apriornyye otsenki u
regulyarnost'
obobahchevuWkh reshedy Aravneniy Monzha-Ampera)
PERIMICAL: Doklak Ahads Nauk '-'SSR, 1957o va.U6, Nr 5, PP.
719-722 (USSR)
ABSTRACT: The autl..e considers the partial differential
equation
(1) rt - a2 a (XPY#z#pPq)1
where ? (XiYPzoPPq):?P Ko> 0 is an a times differentiable
function
(M'>3). Under very nmerous asexuaptions on the function If and
on the solution z (y) the author gives explielt estimations
for
max I z~ and max(grad &). Furthermore the author formulatea a
theorem which asserts that the Irl, lal and~tj in a closed
dcry-ain
can be estimated by the upper bounds of 13-e ) 0 0 4 1 1 ~2
\~ I
? x i ;)q ;e
and by -W(r,) P *(k) (0) (k - 1.2,3,4), Here 9 Is the
polar'angle
Card 1/2 and * (0) is that fun,.cion in which z (x,y) char4es
on the

Apriori-Estimations and Regularity of the Generalized
Solutions 20-5-1/43
of the Equatioas of Yonge-Ampere
boundary of the domain. The obtained estimations are used
in
order to show the regularity of the generalized solution
of (I).
Two Soviet and I foreign references are quoted.
PRESEKT-ED: By V. 1. Sinirnovp Academician~ April 26, 1957
ASSOCIATION:r.eningrad State Pedagogical Institate
(Leningradskiy)
goeudaratvennyy pedagogicheakiy inatitut)
SUMUTM: April 24, 1957
AVAIIMLE: Ubrarj of Congress
Card 2/2

7~7 I-
Y
AUTHORi BALELIMAN,
TITLE: On the Theory of the .onje-Amp6re Zquation
:!onzha-Ampera)
PERIODICAM Vestnik Leningradskogo Universiteta, ',eriii
niki i Astronomii, 19513, fr. 10),P)).25-3tj
(K toorii uravneniy
J.'at(-matikiJ'ekha-
ABSTRACT: In the equation 1)
(1) r t - s' - -P (x,y) (p, q)
f(XPY)> 0 is assumed to be continuous in D and R(p,q),.R,,-
- conat~ 0 to be continuous in the whole p,q-plane. z(XIY) is
assuned to be a twice continuously differentiable solution of
(1). Then the surface t (z - z (x,y)) is convex and has only
one common point with ea-,h supporting plane. The mapping
't(p - Zx ; q - z y) of D into the p,q-plane is one-to-one
continuously differentiable, and for each Borel set VC-D it
holds
r -t - a 2 dx dy dp dq
It Fp, qT RUM
Card 1/3 Since z(x,y) satisfies (1) it holds

On the Theory of the ?Ionav-Amr6re 1,1*quation 43-1-2/10
dp dq
~'~(X,Y) dx dy R(p.q)
too
~~'f(x,y)dx dy is a countib'y additive nonne~:ative set
11
function /,(M) on the Borel sets !! of the domain D, while
di) dQ is a certain set function on It is denoted as
the R-surface of the normal mapping of in symbolst
10 (2) allows to understand the integration of
n(", 4 ) -
(1) as the determination of a convex surface the R-
surface of which is a given countably additive nonnerative
function /t (M) on the ring of the- Borel sets of D. The ge-
neralized solutions of (1) are sought among the general con-
vex surfaces, the R-surface of which is a (,-iven act
function
/(t(M)- By this act up the author aucceeds in applying the
direct methods of A.D. Aleksandrov [Ref.11 ERcf 2] for
tile solution or the, boundary value proble-e for b). -r'or
Card 2/3 stimmable ~(x,y) the author proves with These
methods the

On the Theory of the Monge-Amp4re Equation
43-1-2/1(
solubility of the correspondingly defined Dirichlet
probler.
for (1) and the uniqueneso of the solution in the class of
tho convex functions. 10 theorems are proved on the whole.
4 Soviet references are quoted.
SUBMITTF-D3 28 December 1956
AVAILABLEt Library of Corgrean
1. Conformal mapping 2. Functions 3. Monge-Ampere
equation.-
Theoz7
Card 3/3

AUTHOLS: -k-q&alla4sr-4~~irman,M.Sh.,and SOV/42-13-5-11/1'0
Ladyzhonskaya, O.A.
TITLE: Solomon Grigorlyevich Mikhlin (on the Occasion of his
50th
Birthday) (Solomon Grigor-yevich Mikhlin (K pyatidesyatiletiyu
so dnya, r02hdoniya))
PERIOI;ICAL: Uspekhi matematicheakikh nauk, 1958, Vol 13, Nr
5,pp 215-222 (USSR)
ABSTRACT: This is a short biography and a summary of the
scientific
activity of S.G. Mikhlin with a list of his publications
(1932-1957) containing 78 papers. There is a photo of Mikhlin.
Card 1/1

Ar7THORt
Bakellman, I.Ya. (Leningrad) 20-119-4-1/59
TITLEs
Irregular Surfaoes of Boun4ed Exterior Curvature
(Nereculyar-

nyye poverkhnosti ogr %OM&
ennoy vneahney krivinny)

PERIODICALs
P,
0
Doklady Akademii Nauk /-1
Vol 119
50
Nr ;
631-6,32 (USSR)

,
,
,
, pp
ABSTRACTs
The author considers the following problem set
up by A.D.

Aleksandrovs The class of surfaces with internal
metric of

bounded curvature is to be detnrinined which
contains the follow-

ing oubclaoseat 1. Smooth surfaces of
bounded external curva -

atirej P. general convex surfaces
and surfaces which are repre-

sentable by differences of two
convex functions.

For this purpose the author considers
surfaces F which satis-

fy the following demandst 1. In each
oint X of F the cortin-

gence of the surface forms a cone
K~(X~, the contact cone in X.

Let the sequence fX0 converge
on F to X 0EF, let (Pj be the

sequence of the contact planes
on the cones K,(x
L d' KF(X2)t"

The limit plane P
is the contact plane of K-
(.X
) 2. Each

0
F
o

Point XE F has a neighborhood U which is representable by
Ci%rd 1/ 3

Irregular Surfaces of Bounded Exterior Curvature 20-119-4-1/59
z - f(x1y) under suitable choice of the coordinates, where the
contact cones possess no contact planes in the points of U
which are orthogonal to the x,y-plane. If for such a surface
the positive part of the external curvature is bounded, then
the author denotes these surfaces "surfaces of bounded extern-
al curvature". The class of these s1;,L1'ekceo corresponds to the
demands of the problem set up. Thare hold the following the-
0110mal
Theorems Each point X of a surface F of botinded external cur-
vature possesses a neighborhood UC-F so that there exista a se-
quence of regular surfaces F n with the following properties
1. F n and their internal metrics converee on 11 to F, 2. The
positive parts or the external curvatures (~Kn 4 Sn are uni-
formly bounded. There E n is the set of the points of the F no
where the Gauss ourvature is K 0, d 'n the surface element
of Fn -
Theorems The surfaces of bounded external curvature are wani-
folds of boindod curvature in the sense of A.D. Aleksanerov
with regard to their internal metrics. There are 4 ^Joviet re-
ferences.
Card 2/3

Irregular Surfaces of Bounded Exterior Curvature
20-119-4-1/59
ASSOCIATIONi Laningradakiy gosudarstvennyy pedagogicheskiy
institut imeni
A.I. Gerteena (Leningrad State Pedagogical Institute imeni
AJ, Gerldeen)
PRESENTEDt November 18p 1957p by V.I. Smirnov, Academician
SUBMITTED: November 15, 1957
Card 3/3

AUTHURI 50
TITLEs Definition of a ~Convex Surface bv a Giv-n Function of ~#u
Principal Curvatures (Opredel tkiNv, vypuk.Loy poverkhnosti
dati:ioy
funkteiyoy y9ye glavnykh krivizn)
PERIOI;ICA,.,t Doklady AkademAl nauk SSSR, 1958. Vol 123. lir 2,
pp 21)-2118 jissq)
ABSTRACTs The author investigates the existence of a convex
surface F t~'('
principal our!ratures Ki and K2 of which satisfy -the corA,I.,
(1) f(NIYIZIPtq)KI K2 -%f(.x9y9jjq)(K~' 'K2) -)f(X,Y)
or
(2) f(x,y.a,p,q)K 1X2- T(x,y,p,q)V f(x,y,z,p,q-T(K,+K 2) __Y(xIY)-
where f andfin x and y are, continuku~; in the convex doinain L
f >00 f > 0 and y(x,y) is sumnitAblu in I..
The author introducee the notion of a generalized solution of -
the differentiAl equation (1) and (2). respectively, and it ts
shown that under certain conditions there exist such general-.z.El
solutions which satisfy (1) and (2), respectively, almost
everywhere. The author uses ensentially the investigations of
Alaksandrov /Rnf 1,4'lanu own ..... iA-1
'!here are 4 :;oviet
"ard
1/2

Def in! tion of a Con vox ';urf,,ic(, Iv it G, I v-1
I'vincipal Curvatures
A,:-')OC I AT1 Oil I J,enin,;!rILdLikIy
A. I Gcrtnmi;
1.'.uy 30, 191,43, by V. I rnov, :,c
14ny 28, 1958

BAKEL I K", 1. T&.
Yiret boundary value problem for some nonlinear
elliptic aqua-
tione and Its application to geometrys Uche zap.
Fed. Inst.
Gerts. 1831199-216 1$8. (MMA 13.8)
(Differential squaitions. Partial)

1. Y-.,-., Doe Illyc-L.-Ah Sci
gj=k problt-.. for elli 'Ac o',u: ti~-nv." L:1jdi.L,Ir:-"I
11)5r" - 17 O-ll
170 c 7,i.( ;3jb I ...d -i -, 1
(KL, 100)

16(1)
1UTHORt joakellman. I.Ya. SOV/20-124-2-1/7-1
TITLEt The First Botindary Value Problam for Soma Nozi-Linear
Elliptic
Equationa (Pervaya krayevaya zadacha dlya nokotorykh
nelinzynykh
ellipticheekikh uravneniy)
PERIODICALs Doklady Akademii nauk SSSR, 1959, Vol 124,Nr 2,pp
2401-252 (USSR)
ABSTRACT: The author considers the first boundary value
problem for tha
equation
M F(r9s9t#x9y) - g(xpy)
2 2 2
in the circle Dt x + Y 0.
Some
geometrical applientiontt of the obtkinod rosulta are
given.
There are 4 referencev, 2 of whic.1i .ro Savict, I
Amoricar.,
and I Gorman.
ASSOCIATIONsLeningradskiy gosudarstvernyy institut i-.iuni
A.I.Gertsona (Leningrad State PeCe.~;r~jcal lnntttute imani
A.I.Gertson)
PRESENTED: September 2, 1958, by V.I.Smirnov, AcadeTician
SUBMITTEDs August 25, MO
Card 212

I (,
AUTHOR: --Bakel'man.l.Ya. SOV/20-'26-2-5/E4
IITI,',-": On a Class of Nonlinear Differential Equations
PERIODICAL: Doklady Akad,omii nauk S073R,1959,Vol 126,Nr 2,pp
244-247 (Us5i)
APST IUCT: The author introduces totally elliptio operators
F(,L'),
U #-U nn +U 11 +. . Unn' where uik u 1,6 xibx k 0and
the totally elliptic equations F(u) 0. For F(u) L,! dcfiint-
norn # 0
- - I Pn) ls-~ C (1 +
Card 3A 1.

The Dirichl(~t Problem for ~:on,c;o-Aiap6re "quations
awl Thoir il-Mnonsional Analogues
Then the Dirichlot problem for ('0 is uolvable in the
C;enoralizod senae defined above. Tf~o t:eneralizaLl
solution
satisfies (2) ai.most cver~-,Yherp. 11cre (11)) dcnoteo
the
dia-meter -,f D and it is
k) dpk
There are 3 Soviet references.
A:;:,(#CIAIIION: Leningradskiy pedakroj-,ichea!-ziy
inutitiit imeni A.I. Gerteena
(Leninc;rad Pedar-mical :i,~,d .1,I. Gertscn)
F,!-?bruary 26, 1951), by 7.1. icad,~:Acian
7 D: February 25, 1959
~;nrd 4/4

22858
0 S/044/60/000/012/002/014
LUTHORt -Bak.01,11 Mon. y&. C ill/ C 333
TITLZt The first boundary value problem for some nonlinear
equations of elliptic type and its applications in
geometry. Part I.
PnIODICALt Reforativn7y shurnal, Natematik&~ no. 12, 1960,
78,
abstract 13853-(Uch. sap. Loningr. goo. pod. in-ta in.
A. J. Gertsena, 1958p A
1, 199-216)
TjCXT8 The author considers the first boundary value
preblon
for the nonlinear elliptic uquation F(uX.1 U XY , ayy t X,
Y)-g(x,y)
2 2 A*
in the circle Xx + y '0 R2) or in a bounded oonvex domain,
the
boun"ry of which in regular and possess*@ an essentially
positive
curvature. F in a polynomial of degree 2m +,1 relative-to
u , u
. xx xy
a yy with coefficients from 0(3)(D), y(0,0901z,y)~10. Just
so it is
dom&nj6d, g(.,,y) e 0(3)(D). It in assumed that for-F the
condition
2 2
of strong ellip'lioity Is satisfi:ds 'Pr I + F alp + ro 16
.84 0
2 + 2 ) for every function u( #y) E C 20)) 1 OCO a const >
0
lard 1/2

The first boundary value problem ...
2
0/8 1/012/002/014
4
8/044/6 90
C m/ C 333
dood not depend on the choice ol the function U(xly). The
solubility
of the first boundary value problem is asserted, if the
hi#b*ot terse
of the polynomial@ Ft P j P # 1P, satimfy certain
additional estimation*.
It is stated that the pKaflof ",h* *XiSt*AOO Of the
MaUtiAS can if
carried out according to the We',l-known nth" of
continuation with
respect to a parseeter (S. 1. BerAshtsym, Tu. Bohaudvr
and etkws)t
if at first certain necessary &priori estimation* for the
values of the oolution and of its first and second
derivatives. In tL*
reviewed first part of the ;&W tho-author obtain* the
estimations
of the.values of the solution and of its first
derivatives. As &a
exaxplop satisfying all the requireneikta-imposed by--it
authort the
equation (r+t)3 - 3(rt - S2) (r + t) + (r + t) - g(x, y)
is giveA.
The &*termination of a surface with respect to a given
function
13 + R3 + R + R of the principal radii of curvature R and
I
1 2 1 2 1 2
leado,; to an analogous equation.
[Abstracter's notet complete translation.]
Card 2/2

16i3500, 16.2600
AUTHOR: Bakel Iman,
TITLE: On the
Oil' tile
T( 7 '9 ~"
SOV/142-15-1-5/27
1. Ya.
Stabilit
y Of S01U1,10113 of 1110'1t;e-Ampere H~j,,~ati
Type
PERIODICAL: uspel.,111 wulk, I~Juo, Vol 1~-, Nr 1,
Pi; 1U3-lY()
ABSTRAM Tile authur doi-1-voB eotluiate.3 of ool-.tjolls of
tile
,simplest bloil~;c-Ampere equationst
3
jz) 4 0. Y)
as funeticm~ of ~D(X, y). Equation (1) is examined.
in a convex domain D bounded by a closed convex
curve L., Cp (x, y) I,., a,3surned to be ,;urrLTab).e In D,
and everywhere In D Cp(x, y) > 0. 'P,ww couditiona
Imply that &l. (1) 1.- "A, "I'llptle 11,q)(.' awli that ito
Card 1/5 zqolutlon3 are convex forictlorw,. Ipt Y)

0.-1 tht.~ 11", Al;'p.,w
Equatton"! of the EIIII)t1c, T,-vpt~
lie 1) mtAar
y o C D L,
t tr
4
cavd
Tre
(I I (fit q
C 1)) P,') d471.

On the Stabillt,%, of SAutlon-; Y (7
Equationo of the E1111AIc Type S OV /40 - I I - 5/27
C (1))
4 , (r, y) (h dy V) dX fly.
is derived in, another way. It was first published
by 1U. A. Volkov An the jo-zrna]., Veotnik 1AU Nr 7
( 1 6 0 ) .Tne estimate Eq. (2) trollow~:, directly from
Tiieorem 1: Over. two c-onvex ouvrac(,-6, CD., and 4)2,
dell'iried by thu and -,)(x, y), in
1) ~uzideci corive., D,
a ed~-e and
al,~, 0!1 011C, siae. tile completely
A-(m') an-j
whIch repre"'ent the ".11A Ive Parts,
rk"11"'otively, o!, the varlallo:l ol' t1i,, of
the "et W(q)
I 2
(N)
Ca.-d

Equal loiai of.' th~, Ell-II)t Io T,,pe
D
~!et. hi D. I" atl,i
Ot'. F.
flo
Tiic a;kthov ~l I
(Z) z
a-mined to be
IVC,

"n

D and ab:,,olute
ly o
on, tn
~IOIW
~t 'It
c,!'
n
every I Il, c v va
(a
.

a.,3 it l7kinctlon of' rp(x y) A,, LeVove 1) 1-3 con-.,ey.
and
0, all.-I :;~m able; !I(.%,
y > I M
Card

On the Stability of Solutiotis oC Mjn!,,e-Ampere 777 98
Equatlona of the Elliptic Type S 0 V,/-'42) - 15 - 1 - 5/ 27
generalized solutions of (7) in the bounded
convex domain D, convex onE21-ide zO, a I'p 0. Then 0 )-(2) has at
least one solution.
Theorem 51 Lot (6) be satisfied and lot exist a so > 0
so that
f(xqyjz#ptq):~&2 a2- 1 (04z 0. Then M-M han at least one solution
which does
not vanish identically.
Theorem 6& Lot f(xtzt ) b non-decreasing ir, z;
f(x,y,z)>0 for zz >0
and almost all fxp y5 ~Zrleo Let
f(.,,,'Az).,Xr* f(.,.Y,Z) ((Xalerl ; 0,10,41; Z~rO),
(9)
Card 4/ 7

219!)R
5102 611137100510011026
Non-triv!al solutions ... CiIIYC222
where Xo,(2(1-oO. Then (1)-(2) cannot have more than one
non-negative
solution being not = 0.
Theorem 71 Let exist S 0> 0 and M0> 0 so that
f(x,y,z,p,q)-,,-a3z)f .(fxIyjI6fI ; 04zCSOI -W 0. Then 0)-(2) has at lea3t one solution
beside of
the trivial one.
Theorem 8: Lot exist a sequence R co, so that
f(x,yjz,pjq))o~az" Irl (SRn4- z (R ds
where ri'.* 2 and 6>0 is sufficiently small. Lot exist a
sequence R*_I~O)
n
so that f(xpy,z,ppq)Aa (I+z 2)r2 (0 4 z d,.R*),
n n
where IVI-a( and the an satisfy the condition
Card 5/7

"19.;r
, - J
31"02010/1 _57/005/001/026
Non-trivial solutiona ... C111/C2122
~(I_Ot)an(jt_RI2)"2 ro +jj I
r
o 11 -1 < Rn
where I/r 0is the lower bound of the specific curvature of r.
Then (1)-
(2) has a countable set of different solixtions zn the maxima of
which
increase unboundedly for n -*oD .
The theoreme can be generalized to equations
rt-s2
,W 3 E(x9ypzjpjq~r+2F(xjyjzjpOq)s +
-T7 I
(1+P2 +q ).
+G(x9yjzIppq)t + f(xgy,z,p,q)
and
rt-82
R 7p, 7q
2 2) (0 0( e
where R(p,q) is different from (1+p +q
Card 6/7

S/020/61/137/00,r/001/'026
Non-trivial solutions*.. Cill/C222
There are 6 Soviet-bloo references.
A330CIATIONtVoronezhakiy gosudaretvar-.yy universitet
(Voronezh State
Univezeity)
PRUENTEDs Novomber 23, 196o, by P.S.Aleksatidrov,
Academician
BUBMITTEDt November 22# 1960
Card 7/7

ILIKELIPANY I.Ya.; KWNDSELISKlYp H-A.
Nontrivial so1xitiou Of Dirichlet . problem for
equations with
Mange-Ampere operatork, DokLAN SSSR 137 noOtIOCI-1010 A
161
(A 14&4i
1. Voronesbakiy gooudarstvennyr, miversitat.
Predstavlono akademikom
P.S.Alaksandrovyn,
(Boundary value problems) Iriperatore (Mathematics))

-BAKWMIAN. 1,14,
Generalized ChebyBhev nets and manifolds of bounded
curvature. DAL
AN SSSR 138 no.3:506-507 Fq 161. (MIRA 14:5)
le Leningradakiy gosudarotvonnyy pedagogicheskiy
inotitut in. A.I.
Gertsena. PredstevIeno akademikom V.I.Smirnovym.
(Chebyshev polynomials) (Functiowll analysis)

S/020J61/141/005/001/018
0111/0444
AUTHORt _Bakellman, I Ya.
TITLEt A variation problem connected with Monge-Amp6re
equation
PERIODICAL: Akaaemiya nauk SSSR. Doklady, v. 141, no. 5, 19610
i011 - 1014
TEXTs As it is well known one can obtain the Monge-Ampire
equation 2
xx yy xy 9~(X#
as the Euler equation for certain funotionals. The author
investi-
gates those questions which are connected with the solutions
of the
variation problem for such functionals. Let A be a convex
domain of
the x,y-plan*, its closed and smooth boundary F having the
property
that a tangent on r has only one point in common with r . Lot
C+ be the set of the continuous non-negative functions u(x,
y) which
h
are defined in A + r and equal to the given continuous
function h(X)
on r . Let W+ be the class of the convex functions, being
equal to
h
Card 1/5

S/020/61/141/005/001/016
A variation problem connected with ... 0111 C444
h(X) on r and being convex in the direction of z > 0. Lot
be Z a
cylinder with the directrix r and with f-eneratrices,
parallel to the
z-axis. The function 10) defines a certain closed curve on
Z. It di-
vides Z into the lower domain Z I and the upper domain Z
2' Lot be
u(x, y) F. W11 the uPper boundary of the convex closur* of
ZV Let 1,*
01(u) - , uw(~7, de), w('~, e) being the area of the
normal imtq-e of
A
j(XI Y), et u.,U(de), l(u) - %(u) - 3ffuA(de), (5)
02(u
where~L(e) is a completely additive non-negative
set-function, for
which,tA~.a) < + oo
Theorom ls For every u F- Ch there is 01 (u) 1 (u) t
ID2(u);~ (P2( U)
I(U).> I(-U). The futictional 1(u) is.(iiscontinuous in
the classes
W+ and C+
h h'
Let 5V Ebe the set of all completely additive non-negative
r
Card 2/

8/020~61/141/005/001/018
A variation problem connected with... 0111/C444
~A(o) with the property that "(11) < +OD and /4(JI a ) a 0,
Sit being an
open boundary stripe of A w;th the latitude F_ . Let be W+
the set
of all convex functions from W +, for which W(U, X~) - 0.
hP&
h
Thent
Theorem 2s lf~"(O)c M., then it is suffioient to search the
function for which the functional Z(u) takes an absolute
minimum in
the class W+
h.9- +
Theorem 51 The class W hPE io closed with respect to
uniform conver,
genco,
Theorem 41 1(u) is continuous on w+
h, L
Theorem 5, For every u E. W+ for which Ijuk C -p2max h(X) 0,
h1g,
there hold the following estimationst
) 2, (u) I"<
(u) -.NA CLjju~,(Ju 11, - max h(x) u
Card 3/5

3/020 61/141/005/001/018
A variation problem canneoted with... C111/C444
where the constant C only depends onA, Let u(XP Y) e W" .
Let be
1 h, s.
r,(x Y) a function, twice continuously differevAiable inli.
which
Valli "hes innV Lot -I