Geodesic
Generalized Solutions of Nonlocal Elliptic Problems
Matematičeskie zametki, Tome 77 (2005) no. 5, pp. 665-682

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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 established. 
@article{MZM_2005_77_5_a2,
     author = {P. L. Gurevich},
     title = {Generalized {Solutions} of {Nonlocal} {Elliptic} {Problems}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {665--682},
     publisher = {mathdoc},
     volume = {77},
     number = {5},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2005_77_5_a2/}
}
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P. L. Gurevich. Generalized Solutions of Nonlocal Elliptic Problems. Matematičeskie zametki, Tome 77 (2005) no. 5, pp. 665-682. http://geodesic.mathdoc.fr/item/MZM_2005_77_5_a2/