Regularity theory for the Isaacs equation through approximation methods
Analysis of PDEs
2020-05-19 v2
Abstract
In this paper, we propose an approximation method to study the regularity of solutions to the Isaacs equation. This class of problems plays a paramount role in the regularity theory for fully nonlinear elliptic equations. First, it is a model-problem of a non-convex operator. In addition, the usual mechanisms to access regularity of solutions fall short in addressing these equations. We approximate an Isaacs equation by a Bellman one, and make assumptions on the latter to recover information for the former. Our techniques produce results in Sobolev and H\"older spaces; we also examine a few consequences of our main findings.
Cite
@article{arxiv.1803.01928,
title = {Regularity theory for the Isaacs equation through approximation methods},
author = {Edgard A. Pimentel},
journal= {arXiv preprint arXiv:1803.01928},
year = {2020}
}