On an integral equation for the Dirichlet problem in a plane domain with cusps on the boundary
Sbornik. Mathematics, Tome 68 (1991) no. 1, pp. 61-83 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Integral equations for the Dirichlet problem for the Laplace operator are studied in a plane domain whose boundary has interior or exterior peaks with tangency of first order. Theorems on unique solvability and asymptotics of solutions near the peaks are presented. Bibliography: 8 titles.
@article{SM_1991_68_1_a3,
     author = {V. G. Maz'ya and A. A. Soloviev},
     title = {On an integral equation for the {Dirichlet} problem in a~plane domain with cusps on the boundary},
     journal = {Sbornik. Mathematics},
     pages = {61--83},
     year = {1991},
     volume = {68},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1991_68_1_a3/}
}
TY  - JOUR
AU  - V. G. Maz'ya
AU  - A. A. Soloviev
TI  - On an integral equation for the Dirichlet problem in a plane domain with cusps on the boundary
JO  - Sbornik. Mathematics
PY  - 1991
SP  - 61
EP  - 83
VL  - 68
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/SM_1991_68_1_a3/
LA  - en
ID  - SM_1991_68_1_a3
ER  - 
%0 Journal Article
%A V. G. Maz'ya
%A A. A. Soloviev
%T On an integral equation for the Dirichlet problem in a plane domain with cusps on the boundary
%J Sbornik. Mathematics
%D 1991
%P 61-83
%V 68
%N 1
%U http://geodesic.mathdoc.fr/item/SM_1991_68_1_a3/
%G en
%F SM_1991_68_1_a3
V. G. Maz'ya; A. A. Soloviev. On an integral equation for the Dirichlet problem in a plane domain with cusps on the boundary. Sbornik. Mathematics, Tome 68 (1991) no. 1, pp. 61-83. http://geodesic.mathdoc.fr/item/SM_1991_68_1_a3/

[1] Radon I., “O kraevykh zadachakh dlya logarifmicheskogo potentsiala”, UMN, 1:3–4(13–14) (1946), 96–124 | MR | Zbl

[2] Mazya V. G., “Integralnye uravneniya v teorii potentsiala v oblastyakh s kusochno-gladkimi granitsami”, UMN, 36:4 (1981), 229–230

[3] Mazya V. G., “O razreshimosti granichnykh integralnykh uravnenii teorii uprugosti v oblastyakh s kusochno-gladkimi granitsami”, Differentsialnye uravneniya i ikh prilozheniya. Tr. Vsesoyuzn. simpoz. (Tbilisi. 21–27 aprelya 1982 g.), Metsniereba, Tbilisi, 1986, 123–129 | MR

[4] Adamar Zh., Zadacha Koshi dlya lineinykh uravnenii s chastnymi proizvodnymi giperbolicheskogo tipa, Nauka, M., 1978 | MR

[5] Mazya V. G., Solovev A. A., “Razreshimost integralnogo uravneniya zadachi Dirikhle v ploskoi oblasti s ostriyami na granitse”, DAN SSSR, 298:6 (1988), 1312–1315 | MR | Zbl

[6] Varshavskii S. E., “Konformnoe otobrazhenie beskonechnykh polos”, Matematika (Sb.per.), 2:4 (1958), 67–116

[7] Goluzin G. M., Geometricheskaya teoriya funktsii kompleksnogo peremennogo, Nauka, M., 1966 | MR

[8] Stoilov S., Teoriya funktsii kompleksnogo peremennogo, IL, M., 1962