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.
Cite this article
Giuseppe Mingione, Frank Duzaar, Gradient estimates in non-linear potential theory. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 20 (2009), no. 2, pp. 179–190DOI 10.4171/RLM/540