Lipschitz regularity results for nonlinear strictly elliptic equations and applications
Abstract
Most of lipschitz regularity results for nonlinear strictly elliptic equations are obtained for a suitable growth power of the nonlinearity with respect to the gradient variable (subquadratic for instance). For equations with superquadratic growth power in gradient, one usually uses weak Bernstein-type arguments which require regularity and/or convex-type assumptions on the gradient nonlinearity. In this article, we obtain new Lipschitz regularity results for a large class of nonlinear strictly elliptic equations with possibly arbitrary growth power of the Hamiltonian with respect to the gradient variable using some ideas coming from Ishii-Lions' method. We use these bounds to solve an ergodic problem and to study the regularity and the large time behavior of the solution of the evolution equation.
Keywords
Cite
@article{arxiv.1607.03623,
title = {Lipschitz regularity results for nonlinear strictly elliptic equations and applications},
author = {Olivier Ley and Vinh Duc Nguyen},
journal= {arXiv preprint arXiv:1607.03623},
year = {2016}
}