JournalsrlmVol. 20 , No. 2DOI 10.4171/rlm/540

Gradient estimates in non-linear potential theory

  • Giuseppe Mingione

    Università di Parma, Italy
  • Frank Duzaar

    Universität Erlangen-Nünberg, Germany
Gradient estimates in non-linear potential theory cover

Abstract

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