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arXiv:1404.5156 [math.AP]AbstractReferencesReviewsResources

Generalized solutions of nonlocal elliptic problems

Pavel Gurevich

Published 2014-04-21Version 1

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.

Comments: 18 pages, 2 figures
Journal: Mat. Zametki. 77, No 5 (2005), 665-682; English transl. in Math. Notes 77, No 5-6 (2005), 614-629
Categories: math.AP
Subjects: 35J40, 35J30, 46E35
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