SCIENTIFIC ABSTRACT BITSADZE, A.V. - BITTEL, L.

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R000205410020-7
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 100
• Document Creation Date: November 2, 2016
• Document Release Date: June 9, 2000
• Sequence Number: 20
• Publication Date: December 31, 1967
• Content Type: SCIENCEAB

BITSADZE, AV., RAMUSHEVICH, A.I.; SHAHAT, B.V.
Mikhail Alekseevich Lavrentlev; on his 60th birthday*
Usp. mat.
nauk 16 no.4:211-221 Jl-Ag t61. (FJRA 14:8)
(Lavrent'ev, Mikhail Alekseevich, 1900-)

BITSADW, A.V.
A three-dimensi owl -nal oau of Triconi I s
problem. Sib.
net, sinw, 3 no,5:642-W S-0 162. (MM 15:9)
(Differential equatiolms, Pa*tial)

BITSADZE, A.V.
Mixed type equations In three-dimensional regions. Dokl.
AN SSSR
143 no.5sl0l.7-1019 Ap 162. WRA 15:4)
1. Institut matematiki Sibirskogo otdeleniya AN SSSR.
Chlen-
korrespondent AN SSSR.
(Functiono, Continuous) (Hilbert space)

h5329.
3/020/6VUSAW002/025
MUMS*
AUMlv~ bitesdaws As T.9 VM
TITU* A.homo,#snsous`inclin*d dorivatli to #rolblom for bgrmcmio
fin'Otim
In -thr*o-dIm*nsIosa1 -domain*
PIRIODICALs Aksdemiya-uauk MON. 'balclaidy v.' 1492 00- 49 1963#
749 - 752
TEXT* D denotes a flaiio-simply connected. domain -of 'the
throo-4imoosismal
(19YOS).-space. whiah.16 bouidod.by a1yapunoT.plano C4 continuous
vector.
field'P:- totir) In given. on B.. A function Utz* I,) harmosid in D
is.
P Sy a 1
'is aoutinuous up to the
or derivative.;
.4bught.whicht t6pth with Its first'
bcuAA4ryA and.satieftes thi!conditlon~ ad UePj -vi fohero f is a
9r
continuous fundtiqu giv*n o6 S. -Firstq a review Is of tba -remits
-.on the two4imensional, atoo (Rin9rt probles)l Aheni.*hi
thrds-dimiwiowd'
'lots is
.Cass is studied for, f =0 under the aseumption that 3% the -set
of, PC
*hich'~tbo vector P is%tiagobt to tbi,plaa* St Ay'vot "Ptya,
zarom$slo
'46mose are used,to: derive the, simpli. properties of
Vio,solutions 9 for the
f 012.0wing, cases i condlits.of a single pointo I consists of a
finite,

1; 76,J 11 ~00,1 Ou 0011 003~/ 0 1.1
%.UTHOR. Bitsadze, A. V.
T ITLE: On equations of the mixed composite type.
SOURCE. NeRotoryyc problemy matomatihi i inekhaiiiX-L Nobosibirsk,
Izd-vo
Sib. otd. AN SSSR, 1961, 47-49.
TEXT: The paper deals with the problern of equations of mixed type,
that.is.
c~juatioas which in one part of the region of their validity are
ellipticall, in zm6tlher
part - hyperbolic. The problem is of considerable theoretical and
applicational inn-
i)ortance. If in each point of a rection a differential equation
Nvith pa~._tiai derivatives
iias both real and complex charact'eristics, such an equation is
tcri-ncd "Comn,,niLe."
An equation which in a given region exhibits both characterist4cs
ha6 beci- ter"' ed
by the author and 2vi. S.Salalhitdinov "equations of the
rnixed-compositc type", (Sib.
matem. zh. , v. II, no. 1, 1961, 79-91). The oresent paper
investiga-tes a nunil5br of
problems relative to a model equation of the rni-xed-composite type
T u
--wha-re-T-is -the I-i ne y stated problems for
sets lort -,v correctl
*that equation. The regularity and uniqueness of the solutions
obtained is demonstratc(
the proof of the c.,)dstence of the solutions of the 3 problems
lorn-ailated is reduced to
a one-di-mensional integral equation with special kernels of the
Cauchy type, thle
Card 1/2

On equations of the mixed composite type. S/763/6'L/000/000/003/013
existence of a solution for which in turn is demonstrated on the
basis of the cxisrin,~
theory oi singular integral equations (Muskhelishvili, N. 1. ,
Sinoulyarnyyo iatc grall -
nyye unravneniya [Singular integral enuations] ,
Nloscow-Leningracl, 19-It")). There
are 9 references (the 2 cited Russian-laAguage Soviet, I French-
larguage ard 6
English-language).
Card 212

BITSADZE AS
Pamogeneous probIew of an inclined derivative for
harmonic
--functions in threazdijonsional regions. Dokl.AN
SSSR 148
no-41749-752 F 163. (MMA 164)
1. Tnstitut matematiki Sibirskogo otdeleniya AN
SSSR. Chlen-
korreapondent AN SSSR. (Harmonic functions)
.-.All

ACCESSION NR: AP4030771 3/0020/64/155/004/073010731
_pk4dze,__A. V. (Corresponding member)
AUTHOR:
TITLE: On a special case of the problem of directional derivatives
for harmonic
functions in three-dimensional regions
SOURCE: AN SSSR. Doklady*o v, 155, no. 4, 1964, 730-731
TOPIC TAGS: elliptic differential equation , harmonic function
partial
differential equation , boundary value problem
ABSTRACT: Let D be a bounded, simply connected re&ion in the
(x,y,z) space,
bo6ded by a Lyapunov Surface S rnot'defined here and let A be the
point (d,0,01,
or some cynstant a. The problem- is to find a reg7ular harmonic
function U(X,Y,Z),
f
of class C in D +S and such that its direction derivative in the
direction of
the vector AP has a given value at each point P of S. Since the
expression
(x-a)U- + yU 4 zU is itself a regular harmonic function in D, the
problem reduces
to finlina aysolutfon U of the first order linear equation
(x a) U. + mUs, + XV. V (x, y. z). (x, M, z) e D.,
1/4
Card

! ACCESSION NR: AP4030771
which is harmonic. V (s.y,s) is the known harm.onic function
in D which takea~
the g ven boundary~ values f on So Assume now that V is the
ball D with boundary
S: xi + Y a:2 a; Case 1. 1 a -C 1. The probles' has
solutions, given by
(x, Y. 3) ~V (a + I (x 0), ty,
for arbitrary constant C, if, and only if, f satisfies the
condition
V (a. 0, 011
(i + 62-32CMI)MIds 0. (3)
S
and if the condition is satisfied, there are no other
solutions. Case 2. 1 ap- 1.0
The solution Ls given by
(4)
where V is a function of class C2 in the variables which must
Card 214

ACCESSION UR: AP4030771
satisfy a certain elliptic second order linear equation. The
solution is uniquely
V a 4
determined by its values along the circle( + It a -4g- ) of contact
of the sphere
S with the circumscribed cone of vertex A. (For the
uniqueness'statements, the
reader is referred to earlier papers by the author.) Additional
remarks- (1) The
results are similar if instead of the vector (x-a, y, z), one
considers the vector
(p#q,r), where
p-p~+ax+by+cz, q-qg-bx+ay+dz. r-r~-cj;-dy+az.
A2) The degree of deteminatLon of the solution depends on the
Kronecker index of
vector (p,q,r). (In the case dLscuseed here, the index is +1 if jai
e. 1, 0 if
I al > 1.) This question is to be treated in a future paper. Orig.
art. has: 6'
equations.
ASSOCIATIONt Institut matematiki tibirskogo otdolenLys AN SSSR
(Institute,*of
Mathematics vith Cum uter Center$ Siberian Division, AN SSSR)
p
d
,Car
3/4

ACCESSION NR: AP4030771
SUMMED: 03J&a~ 'DATZ ACQ: Mor64 ENCL: 00
SUB CODE mi NO SW sovt 001 OTHER: 001

partial
rent

=M-U
UZ
-AM ZM
2 i-MM-N

L 7 9 - 7-r T -P'
TT`-F -7- 7 r L- c- rr. I i ned de ri vaL i ve wi t'~~
S ~D rLT, C S 1 a',3%, 157, no . 6, 1-964, 1 -2 '7 _3
TOPT-C TA--S: fe rent i a I equ at i on , p c) I y n om.a
Fk TP-A -7 -T") t o f i n d a f r. c ton
b'D u 5,j,3

L 6'? 93-65
ACCFSSION AS 404 486 9
-luous f!i.,~ -
ql~
'y2j
raaU
g -(y) is defined As the limit of gradv(x) as X Y,
taine-d in D. Tt
is 5-hown that the p r ob I ern; ~, an 1,,
r W, grad U W =1,111),
the right e; 3. de nf w~n I -,~s a function which is ;~rl i~ r,,-
-~,zk is _i rv-7
Showm flA.--ler
Cnrd 2/3

-'IS t 1 t u t "natematiki S ibi rskoq,-~

BITSADZE, A.V.
A class of multidimensional singular Integral
SqUationse DOkle
AN SSSR 159 no.51955-957 D 164 (MTRA 18tl)
1, Institut m*tsmatiki Sibirskogo otdeleniya AN
SSSR, Chlen-
korrespondent AN SSSR9
w*

BKtS, Lipman; BITSADEZE, A.V., red.
[Mathematical problems of subsonic end
transonic gas
dynamics] Matematicheakie voprosy dozvukovoi i
okolo-
zvukovoi dinamiki. Moskva, Izd-vo :Lnostr.
lit-ryp 1961.
208 p. (MIRA 17:4)

EWT(d) jjp(c)
"ACC NR, ~)P6016359 SOURCE CODE: UR/002_0/65/164/006A~18/122C
22
AUTHOR:- Bitsadzej, A. V, (C rresponding member AN'SSSR)
ORG; Institute of Mathematies0barian' Branch, AN SSSR
(Institut matematiki
.5ibirskogo otdeleniya AN SSSR)
TITLE: Normally solvable elliptic bound value Problems
SOURCE: AN SSSR. 'Doklady, v. 164, no. 6, 1965P~121 8-1220
TOPIC TAGS: boundary value probleml, mathematics
ABSTRACT: In -the opInioh'of.the.auth6r' o'h'e'-o'f the
6ential q'u*e'stions
; n
',,i__tSe theo:ry of elliptic boundary Value problems Is
finding tests
,of normal solvability. No less'important Is the question of
es-
itablishing the degree of overdetermination'or
underdetermination of
.a particular boundary value problem* An Important, but by no
means
decisive, factor leading to a solution-of the latter question
Is
the calculation*of the index YL of a Noetherian problem.
.Tests.of Noetherianism and Fredh6lmlanism have at present been
established only for Individual olas-ses of elliptic boundary
value
-problems Noetherianism to violated eVen'In the case
of-elliptic
.operators with two Independent v"Iables.- A simplp example of
'non-Noetherian problems normally solvable in.the Hausdortf
sense
Is the Dirlohlet, problem
Ul (t)
C&d 1/2 UDC: 517-946

ACC NRs AP6016359
',for the elliptic system -:2
asul
24 .0501, Pus
+ hot
-dIfferentlable 1h thei
4here'h and h2 are functions continuously
Circle 'm Z.-I