Solvability of nonlocal elliptic problems in Sobolev spaces

Abstract

We study elliptic equations of order $2m$ with nonlocal boundary-value conditions in plane angles and in bounded domains, dealing with the case where the support of nonlocal terms intersects the boundary. We establish necessary and sufficient conditions under which nonlocal problems are Fredholm in Sobolev spaces and, respectively, in weighted spaces with small weight exponents. We also obtain an asymptotics of solutions to nonlocal problems near the conjugation points on the boundary, where solutions may have power singularities.