On the viscosity solutions to some nonlinear elliptic equations
Analysis of PDEs
2016-10-13 v2
Abstract
We consider viscosity solutions of a class of nonlinear degenerate elliptic equations on bounded domains. We prove comparison principles and a priori supremum bounds for the solutions. We also address the eigenvalue problem and, in many instances, show the existence of a first eigenvalue and a first positive eigenfunction.
Keywords
Cite
@article{arxiv.1503.04879,
title = {On the viscosity solutions to some nonlinear elliptic equations},
author = {Tilak Bhattacharya and Leonardo Marazzi},
journal= {arXiv preprint arXiv:1503.04879},
year = {2016}
}
Comments
33 pages. The work underwent a significant revision. The work has been expanded and generalized, relevant examples included and important references added