An elliptic boundary value problem with fractional nonlinearity
Analysis of PDEs
2020-05-20 v1
Abstract
We investigate existence and uniqueness of solutions to second-order elliptic boundary value problems containing a power nonlinearity applied to a fractional Laplacian. We detect the critical power separating the existence from the non-existence regimes. For the existence results, we make use of a particular class of weighted Sobolev spaces to compensate boundary singularities which are naturally built in the problem.
Cite
@article{arxiv.2005.09515,
title = {An elliptic boundary value problem with fractional nonlinearity},
author = {Nicola Abatangelo and Matteo Cozzi},
journal= {arXiv preprint arXiv:2005.09515},
year = {2020}
}
Comments
21 pages