Geodesic
On a method of solving boundary value problems for elliptic systems of second-order differential equations in the plane
Sbornik. Mathematics, Tome 18 (1972) no. 4, pp. 603-620 
N. E. Tovmasyan. On a method of solving boundary value problems for elliptic systems of second-order differential equations in the plane. Sbornik. Mathematics, Tome 18 (1972) no. 4, pp. 603-620. http://geodesic.mathdoc.fr/item/SM_1972_18_4_a4/
@article{SM_1972_18_4_a4,
     author = {N. E. Tovmasyan},
     title = {On a~method of solving boundary value problems for elliptic systems of second-order differential equations in the plane},
     journal = {Sbornik. Mathematics},
     pages = {603--620},
     year = {1972},
     volume = {18},
     number = {4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1972_18_4_a4/}
}
TY  - JOUR
AU  - N. E. Tovmasyan
TI  - On a method of solving boundary value problems for elliptic systems of second-order differential equations in the plane
JO  - Sbornik. Mathematics
PY  - 1972
SP  - 603
EP  - 620
VL  - 18
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/SM_1972_18_4_a4/
LA  - en
ID  - SM_1972_18_4_a4
ER  - 
%0 Journal Article
%A N. E. Tovmasyan
%T On a method of solving boundary value problems for elliptic systems of second-order differential equations in the plane
%J Sbornik. Mathematics
%D 1972
%P 603-620
%V 18
%N 4
%U http://geodesic.mathdoc.fr/item/SM_1972_18_4_a4/
%G en
%F SM_1972_18_4_a4

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

In this work we describe a new method of solving boundary value problems for elliptic systems of second-order differential equations in the plane. The new method is illustrated for the case of an exterior Dirichlet problem for an elliptic system with constant coefficients. By means of this method we obtain an explicit form of the solution of exterior problems of Dirichlet and of Neumann, and we establish an effective method of solving more general boundary value problems for systems of differential equations with constant coefficients in domains which are bounded by an ellipse. Bibliography: 8 titles.

[1] A. V. Bitsadze, Kraevye zadachi dlya ellipticheskikh uravnenii vtorogo poryadka, Nauka, Moskva, 1966

[2] I. N. Vekua, Novye metody resheniya ellipticheskikh uravnenii, Gostekhizdat, Moskva, 1948 | MR

[3] A. M. Volpert, “Obschie predstavleniya reshenii ellipticheskoi sistemy uravnenii s postoyannymi koeffitsientami”, Sb. nauchn. trudov Lvovskogo lesotekhn. in-ta, IV (1959), 111–122

[4] N. I. Muskhelishvili, Singulyarnye integralnye uravneniya, Nauka, Moskva, 1968 | MR | Zbl

[5] L. I. Chibrikova, V. S. Rogozhin, O svedenii nekotorykh kraevykh zadach k obobschennoi zadache Rimana, Uch. zap. Kazansk. un-ta, 112, no. 10, 1952 | MR

[6] I. G. Petrovskii, Lektsii po teorii obyknovennykh differentsialnykh uravnenii, Nauka, Moskva, 1964 | MR | Zbl

[7] I. G. Petrovskii, Lektsii po teorii integralnykh uravnenii, Gostekhizdat, Moskva, 1951 | MR

[8] N. E. Tovmasyan, Zadacha Dirikhle dlya ellipticheskikh sistem differentsialnykh uravnenii vtorogo poryadka, ne udovletvoryayuschikh usloviyu Ya. B. Lopatinskogo, 1966