Correctness of the local boundary value problem in a cylindrical domain for Laplace's many-dimensional equation

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 paper, using authors early methods we prove a unique solvability of the local boundary value problem in the cylindric domain for a Laplace's many-dimensional equation which is a generalization of the Dirichlet and Poincare problems. besides, the criterion of uniqueness of the regular solution is obtained.