Positive solutions of nonlinear problems involving the square root of the Laplacian
Analysis of PDEs
2009-05-11 v1
Abstract
We consider nonlinear elliptic problems involving a nonlocal operator: the square root of the Laplacian in a bounded domain with zero Dirichlet boundary conditions. For positive solutions to problems with power nonlinearities, we establish existence and regularity results, as well as a priori estimates of Gidas-Spruck type. In addition, among other results, we prove a symmetry theorem of Gidas-Ni-Nirenberg type.
Keywords
Cite
@article{arxiv.0905.1257,
title = {Positive solutions of nonlinear problems involving the square root of the Laplacian},
author = {Xavier Cabre and Jinggang Tan},
journal= {arXiv preprint arXiv:0905.1257},
year = {2009}
}