A Dirichlet problem for nonlocal degenerate elliptic operators with internal nonlinearity
Analysis of PDEs
2016-02-09 v1
Abstract
We study a Dirichlet problem in the entire space for some nonlocal degenerate elliptic operators with internal nonlinearities. With very mild assumptions on the boundary datum, we prove existence and uniqueness of the solution in the viscosity sense. If we further assume uniform ellipticity then the solution is shown to be classical, and even smooth if both the operator and the boundary datum are smooth.
Cite
@article{arxiv.1602.02341,
title = {A Dirichlet problem for nonlocal degenerate elliptic operators with internal nonlinearity},
author = {Hui Yu},
journal= {arXiv preprint arXiv:1602.02341},
year = {2016}
}
Comments
18 pages