Well-posedness of the Dirichlet problem for a class of multidimensional elliptic-parabolic equations

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 work, the method proposed in the author’s works, shows the unique solvability and obtained the explicit form of the Dirichlet problem in the cylindric domain for a class of multidimensional elliptic-parabolic equations.