Existence and multiplicity for elliptic problems with quadratic growth in the gradient
Analysis of PDEs
2012-10-25 v2
Abstract
We show that a class of divergence-form elliptic problems with quadratic growth in the gradient and non-coercive zero order terms are solvable, under essentially optimal hypotheses on the coefficients in the equation. In addition, we prove that the solutions are in general not unique. The case where the zero order term has the opposite sign was already intensively studied and the uniqueness is the rule.
Cite
@article{arxiv.1010.4520,
title = {Existence and multiplicity for elliptic problems with quadratic growth in the gradient},
author = {Louis Jeanjean and Boyan Sirakov},
journal= {arXiv preprint arXiv:1010.4520},
year = {2012}
}
Comments
To appear in Comm. PDE