H\^older continuity of solutions of second-order non-linear elliptic integro-differential equations
Analysis of PDEs
2010-09-06 v1
Abstract
This paper is concerned with H\"older regularity of viscosity solutions of second-order, fully non-linear elliptic integro-differential equations. Our results rely on two key ingredients: first we assume that, at each point of the domain, either the equation is strictly elliptic in the classical fully non-linear sense, or (and this is the most original part of our work) the equation is strictly elliptic in a non-local non-linear sense we make precise. Next we impose some regularity and growth conditions on the equation. These results are concerned with a large class of integro-differential operators whose singular measures depend on and also a large class of equations, including Bellman-Isaacs Equations.
Keywords
Cite
@article{arxiv.1009.0685,
title = {H\^older continuity of solutions of second-order non-linear elliptic integro-differential equations},
author = {Guy Barles and Emmanuel Chasseigne and Cyril Imbert},
journal= {arXiv preprint arXiv:1009.0685},
year = {2010}
}