Generalized solutions of nonlocal elliptic problems
  An elliptic equation of order $2m$ with general nonlocal boundary-value conditions, in a plane bounded domain $G$ with piecewise smooth boundary, is considered. Generalized solutions belonging to the Sobolev space $W_2^m(G)$ are studied. The Fredholm property of the unbounded operator corresponding to the elliptic equation, acting on $L_2(G)$, and defined for functions from the space $W_2^m(G)$ that satisfy homogeneous nonlocal conditions is proved. 
Pavel Gurevich
math.AP