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

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

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 b...

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Bibliographic Details
Main Author: Бурский, В.П.
Format: Article
Language:Russian
Published: Інститут математики НАН України 1993
Series:Український математичний журнал
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Online Access:http://dspace.nbuv.gov.ua/handle/123456789/156430
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Summary: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.

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