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arXiv · 1404.5156

Generalized solutions of nonlocal elliptic problems

Pavel Gurevich
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Abstract

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.

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Pavel Gurevich. 2014-04-21. Generalized solutions of nonlocal elliptic problems. https://arxiv.org/abs/1404.5156

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