Global solvability of the Laplace equation in weighted Sobolev spaces

We consider a non-local boundary value problem for the Laplace equation in unbounded domain. We are interested for the weak solvability of that problem in the framework of weighted Sobolev spaces with Muckenhoupt weight. We proved that any weak solution belonging to suitable weighted Sobolev space is also a strong solution and satisfies the corresponding boundary conditions, extending in such a way the classical results. It should be noted that such problems do not fit into the general theory of elliptic equations and require a special technique.