Geodesic
On the theory of the Carleman–Vekua equation with a singular point
Sbornik. Mathematics, Tome 78 (1994) no. 2, pp. 357-365 
A. Tungatarov. On the theory of the Carleman–Vekua equation with a singular point. Sbornik. Mathematics, Tome 78 (1994) no. 2, pp. 357-365. http://geodesic.mathdoc.fr/item/SM_1994_78_2_a4/
@article{SM_1994_78_2_a4,
     author = {A. Tungatarov},
     title = {On the theory of {the~Carleman{\textendash}Vekua} equation with a~singular point},
     journal = {Sbornik. Mathematics},
     pages = {357--365},
     year = {1994},
     volume = {78},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1994_78_2_a4/}
}
TY  - JOUR
AU  - A. Tungatarov
TI  - On the theory of the Carleman–Vekua equation with a singular point
JO  - Sbornik. Mathematics
PY  - 1994
SP  - 357
EP  - 365
VL  - 78
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SM_1994_78_2_a4/
LA  - en
ID  - SM_1994_78_2_a4
ER  - 
%0 Journal Article
%A A. Tungatarov
%T On the theory of the Carleman–Vekua equation with a singular point
%J Sbornik. Mathematics
%D 1994
%P 357-365
%V 78
%N 2
%U http://geodesic.mathdoc.fr/item/SM_1994_78_2_a4/
%G en
%F SM_1994_78_2_a4

Voir la notice de l'article provenant de la source Math-Net.Ru

An integral representation is constructed and sufficient conditions are obtained for the existence of continuous solutions of the Carleman–Vekua equation with a singular point. The Riemann–Hilbert problem is analyzed for such an equation in the class of continuous functions.

[1] Mikhailov L. G., Novyi klass osobykh integralnykh uravnenii i ego prilozheniya k differentsialnym uravneniyam s singulyarnymi koeffitsientami, Irfon, Dushanbe, 1963

[2] Usmanov Z. D., “Beskonechno malye izgibaniya poverkhnostei polozhitelnoi krivizny s tochkoi uploscheniya”, Differential Geometry, Banach Center Publications, 12, Warsaw, 1984, 241–272 | MR | Zbl

[3] Usmanov Z. D., “O beskonechno malykh izgibaniyakh poverkhnostei polozhitelnoi krivizny s izolirovannoi tochkoi uploscheniya”, Matem. sb., 83 (125):4 (12) (1970), 596–615 | MR | Zbl

[4] Vekua I. N., Obobschennye analiticheskie funktsii, Fizmatgiz, M., 1959 | MR

[5] Usmanov Z. D., “Ob odnom klasse obobschennykh sistem Koshi–Rimana s singulyarnoi tochkoi”, Sib. matem. zhurnal., 14:5 (1973), 1076–1087 | MR | Zbl

[6] Monakhov V. N., Kraevye zadachi so svobodnymi granitsami dlya ellipticheskikh sistem uravnenii, Nauka, Novosibirsk, 1977 | MR

[7] Bitsadze A. V., Osnovy teorii analiticheskikh funktsii kompleksnogo peremennogo, Nauka, M., 1984 | MR