Gradient estimates in non-linear potential theory

Abstract

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.