Solvability Dirichlet problem for three-dimensional elliptic-parabolic equations with type and order extinction

Abstract

Correctness of boundary problems in the plane for elliptic equations is well analyzed by analitic function theory of complex variable. There appear principal difficulties in similar problems when the number of independent variables is more than two. An attractive and suitable method of singular integral equations is less strong because of lock of any complete theory of multidimensional singular integral equations. In the works of S.A. Aldasheva, shows the unique solvability and obtained form of the explicit Dirichlet problem in the cylindrical domain for multidimensional elliptic-parabolic equations. In this paper, for the three-dimensional elliptic-parabolic equations with degeneration of the type and order in a cylindrical domain shown solvability and obtained in the form of a classical solution of the Dirichlet problem.