Smoothness of generalized solutions for nonlocal elliptic problems on the plane

We study smoothness of generalized solutions of nonlocal elliptic problems in plane bounded domains with piecewise smooth boundary. The case where the support of nonlocal terms can intersect the boundary is considered. We announce conditions that are necessary and sufficient for any generalized solution to possess an appropriate smoothness (in terms of Sobolev spaces). The proofs are given in the forthcoming paper.