О краевых задачах для эллиптического уравнения с комплексными коэффициекгами и одной проблеме моментов

• Veröffentlicht in: Український математичний журнал
• Datum: 1993
• 1. Verfasser: Бурский, В.П.
• Format: Artikel
• Sprache: Russisch
• Veröffentlicht: Інститут математики НАН України 1993
• Schlagworte: Статті
• Online Zugang: https://nasplib.isofts.kiev.ua/handle/123456789/156430
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Zitieren: О краевых задачах для эллиптического уравнения с комплексными коэффициекгами и одной проблеме моментов / В.П. Бурский // Український математичний журнал. — 1993. — Т. 45, № 11. — С. 1476–1483. — Бібліогр.: 11 назв. — рос.

Elliptic systems of two second-order equations, which can be written as a single equation with complex coefficients and a homogeneous operator, are studied. The necessary and sufficient conditions for the connection of traces of a solution are obtained for an arbitrary bounded domain with a smooth boundary. These conditions are formulated in the form of a certain moment problem on the boundary of a domain; they are applied to the study of boundary-value problems. In particular, it is shown that the Dirichlet problem and the Neumann problem are solvable only together. In the case where the domain is a disk, the indicated moment problem is solved together with the Dirichlet problem and the Neumann problem. The third boundary-value problem in a disk is also investigated.