Gradient estimates in non-linear potential theory
Analysis of PDEs
2009-06-29 v1
Abstract
We present pointwise gradient bounds for solutions to -Laplacean type non-homogeneous equations employing non-linear Wolff type potentials, and then prove similar bounds, via suitable caloric potentials, for solutions to parabolic equations. A method of proof entails a family of non-local Caccioppoli inequalities, together with a DeGiorgi's type fractional iteration.
Cite
@article{arxiv.0906.4943,
title = {Gradient estimates in non-linear potential theory},
author = {Frank Duzaar and Giuseppe Mingione},
journal= {arXiv preprint arXiv:0906.4943},
year = {2009}
}