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Boundary-value problems for an elliptic equation with complex coefficients and a certain moment problem

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Abstract

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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Authors and Affiliations

  1. Institute of Applied Mathematics and Mechanics, Ukrainian Academy of Sciences, Donetsk

    V. P. Burskii

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  1. V. P. Burskii
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Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 11, pp. 1476–1483, November, 1993.

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Burskii, V.P. Boundary-value problems for an elliptic equation with complex coefficients and a certain moment problem. Ukr Math J 45, 1659–1668 (1993). https://doi.org/10.1007/BF01060856

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  • DOI: https://doi.org/10.1007/BF01060856

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