The consistency conditions and the smoothness of generalized solutions of nonlocal elliptic problems
Analysis of PDEs
2014-04-22 v1
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.
Keywords
Cite
@article{arxiv.1404.5162,
title = {The consistency conditions and the smoothness of generalized solutions of nonlocal elliptic problems},
author = {Pavel Gurevich},
journal= {arXiv preprint arXiv:1404.5162},
year = {2014}
}
Comments
39 pages, 5 figures