Gradient estimates in non-linear potential theory

Details Gradient estimates in non-linear potential theory Gradient estimates in non-linear potential theory

2009-06-26

arxiv.org/abs/0906.4943v1

Rendiconti Lincei - Matematica e Applicazioni, 20 (2009) 179-190

Mathematics

Analysis of PDEs

Scientific paper

We present pointwise gradient bounds for solutions to $p$-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.

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