Abstract
This article shows the unique solvability and obtains an explicit form of the classical solution of the mixed prob-lem in a cylindrical domain for a model degenerate multidimensional elliptic equation. The correctness of boundary value problems in the plane for elliptic equations by the method of the theory of ana-lytic functions of a complex variable has been well studied. The first boundary value problem or the Dirichlet problem for multidimensional elliptic equations with degeneration on the boundary has been sufficiently analyzed. However, as we know, the mixed problem for the indicated equations has been studied very little.