Uniform bounds via regularity estimates for elliptic PDE with critical growth in the gradient
Analysis of PDEs
2015-09-16 v1
Abstract
We prove non-uniqueness and study the behaviour of viscosity solutions of a class of uniformly elliptic fully nonlinear equations of Hamilton-Jacobi-Bellman-Isaacs type, with quadratic growth in the gradient. The crucial a priori bound for the solutions is proved through an argument which uses a boundary growth lemma, and consequences such as boundary "half"-Harnack inequalities, which are of independent interest. Our results are new even for linear equations.
Keywords
Cite
@article{arxiv.1509.04495,
title = {Uniform bounds via regularity estimates for elliptic PDE with critical growth in the gradient},
author = {Boyan Sirakov},
journal= {arXiv preprint arXiv:1509.04495},
year = {2015}
}
Comments
9 pages