Boundary-value problems for an elliptic equation with complex coefficients and a certain moment problem
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.
English version (Springer): Ukrainian Mathematical Journal 45 (1993), no. 11, pp 1659-1668.
Citation Example: Burskii V. P. Boundary-value problems for an elliptic equation with complex coefficients and a certain moment problem // Ukr. Mat. Zh. - 1993. - 45, № 11. - pp. 1476–1483.