Advances in Differential Equations

The consistency conditions and the smoothness of generalized solutions of nonlocal elliptic problems

Pavel Gurevich

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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.

Article information

Source
Adv. Differential Equations Volume 11, Number 3 (2006), 305-360.

Dates
First available in Project Euclid: 18 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355867712

Mathematical Reviews number (MathSciNet)
MR2221485

Zentralblatt MATH identifier
1194.35124

Subjects
Primary: 35J25: Boundary value problems for second-order elliptic equations
Secondary: 35B65: Smoothness and regularity of solutions 35D10

Citation

Gurevich, Pavel. The consistency conditions and the smoothness of generalized solutions of nonlocal elliptic problems. Adv. Differential Equations 11 (2006), no. 3, 305--360. https://projecteuclid.org/euclid.ade/1355867712.


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