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

  • V. P. Burskii

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.
Published
25.11.1993
How to Cite
BurskiiV. P. “Boundary-Value Problems for an Elliptic Equation With Complex Coefficients and a Certain Moment Problem”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 45, no. 11, Nov. 1993, pp. 1476–1483, https://umj.imath.kiev.ua/index.php/umj/article/view/5954.
Section
Research articles