Advances in Differential Equations
- Adv. Differential Equations
- Volume 11, Number 3 (2006), 305-360.
The consistency conditions and the smoothness of generalized solutions of nonlocal elliptic problems
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.
Adv. Differential Equations, Volume 11, Number 3 (2006), 305-360.
First available in Project Euclid: 18 December 2012
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 35J25: Boundary value problems for second-order elliptic equations
Secondary: 35B65: Smoothness and regularity of solutions 35D10
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