Geodesic
Elliptic problems with nonlocal conditions near the boundary
Sbornik. Mathematics, Tome 57 (1987) no. 1, pp. 293-316

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An elliptic equation of order $2m$ with nonlocal conditions near the boundary is considered. The presence of nonlocal terms in the boundary conditions leads to the appearance of singularities in the solution. The Noether property is proved for this problem in weighted spaces and asymptotics of the solutions are obtained. These results are applied to the study of the solvability and smoothness of solutions of elliptic differential-difference equations. Bibliography: 22 titles. 
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     author = {A. L. Skubachevskii},
     title = {Elliptic problems with nonlocal conditions near the boundary},
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A. L. Skubachevskii. Elliptic problems with nonlocal conditions near the boundary. Sbornik. Mathematics, Tome 57 (1987) no. 1, pp. 293-316. http://geodesic.mathdoc.fr/item/SM_1987_57_1_a18/