Abstract:
Correct statements of boundary value problems on the plane for elliptic equations by the method of the theory of analytic functions of a complex variable are well studied. In the study of similar issues, when the number of independent variables is more than two, there are difficulties of a fundamental nature. The very attractive and convenient method of singular integral equations loses its force due to the absence of any complete theory of multidimensional singular integral equations. The author has previously studied local boundary value problems in a cylindrical domain for multidimensional elliptic equations. In this article, the method proposed in the author's earlier works is used. The unique solvability is shown and an explicit form of the classical solution of a mixed problem in a cylindrical domain for a single class of degenerate multidimensional elliptic equations is obtained. A criterion for the uniqueness of a regular solution of these problems was also obtained.
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