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2006 The consistency conditions and the smoothness of generalized solutions of nonlocal elliptic problems
Pavel Gurevich
Adv. Differential Equations 11(3): 305-360 (2006).

Abstract

We study smoothness of generalized solutions of nonlocal elliptic problems in plane bounded domains with piecewise smooth boundary. The case where the support of nonlocal terms can intersect the boundary is considered. We find conditions that are necessary and sufficient for any generalized solution to possess an appropriate smoothness (in terms of Sobolev spaces). Both homogeneous and nonhomogeneous nonlocal boundary-value conditions are studied.

Citation

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Pavel Gurevich. "The consistency conditions and the smoothness of generalized solutions of nonlocal elliptic problems." Adv. Differential Equations 11 (3) 305 - 360, 2006.

Information

Published: 2006
First available in Project Euclid: 18 December 2012

zbMATH: 1194.35124
MathSciNet: MR2221485

Subjects:
Primary: 35J25
Secondary: 35B65, 35D10

Rights: Copyright © 2006 Khayyam Publishing, Inc.

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Vol.11 • No. 3 • 2006
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