Entire solutions of fully nonlinear elliptic equations with a superlinear gradient term
Analysis of PDEs
2015-06-24 v1
Abstract
In this paper we consider second order fully nonlinear operators with an additive superlinear gradient term. Like in the pioneering paper of Brezis for the semilinear case, we obtain the existence of entire viscosity solutions, defined in all the space, without assuming global bounds. A uniqueness result is also obtained for special gradient terms, subject to a convexity/concavity type assumption where superlinearity is essential and has to be handled in a different way from the linear case.
Keywords
Cite
@article{arxiv.1506.06994,
title = {Entire solutions of fully nonlinear elliptic equations with a superlinear gradient term},
author = {Giulio Galise and Shigeaki Koike and Olivier Ley and Antonio Vitolo},
journal= {arXiv preprint arXiv:1506.06994},
year = {2015}
}