  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.
