H\"older regularity for non-variational porous media type equations
Analysis of PDEs
2022-09-15 v2
Abstract
We present a Krylov-Safonov theory approach for the H\"older regularity of viscosity solutions to non-variational porous media type equations. We explore the peculiarity of this type of problem: either the equation falls in a uniformly elliptic regime or the eikonal mechanism takes care of the regularity. Our techniques are based on sliding paraboloids resulting in an ABP-type measure estimate. By combining such estimates, a diminishing of oscillation property is available, resulting in a regularity control in H\"older spaces.
Keywords
Cite
@article{arxiv.2108.00464,
title = {H\"older regularity for non-variational porous media type equations},
author = {Héctor A. Chang-Lara and Makson S. Santos},
journal= {arXiv preprint arXiv:2108.00464},
year = {2022}
}