A new method for studying the boundary value problem for athree-dimensional elliptic equation with variable coefficients

The paper is devoted to the study of the Fredholm property of a boundary value problem for a three-dimensional elliptic equation with variable coefficients with nonlocal boundary conditions in a bounded domain with a Lyapunov boundary.Singular necessary solvability conditions are derived, the regularization of which is carried out according to a new original scheme.Based on the regularized necessary conditions and boundary conditions, the Fredholm property of the problem is proved.