A boundary value problem for singular second order elliptic equation on a bounded domain with boundary angular points

In the paper we consider a singular elliptic partial differential equation of the second order. It is studied on a bounded plain domain with boundary corner points. A type of the differential equation is defined by its singular coefficients. A differential equation contains the Bessel operator acting by a special variable. Problems formulations use special functions of hypergeometric type, namely adjoint Legendre functions for solutions representations. The applied functional spaces with mixed norms are of Sobolev-Kipriyanov class with additional boundary conditions. Also a priori estimates are proved for solutions of considered differential equations with boundary conditions in functional spaces. A plan is outlined for solving representation formulas for problem solutions in terms of series in adjoint Legendre functions. The result is proved on correctness of the problem considered in weighted functional spaces. The procedure includes such steps as a proper special change of variables, application of Fourier transform, consideration of the Green function for some special ordinary type differential equation with complex parameter, which is considered on the strip of the plane in new variables.