English

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

R2 v1 2026-06-22T08:54:44.236Z