Gradient estimates via non-linear potentials

TL;DR

This paper develops pointwise gradient bounds for solutions to non-linear PDEs like p-Laplace equations using non-linear potentials, extending these bounds to parabolic equations with caloric potentials.

Contribution

It introduces novel gradient estimates for non-linear PDEs using non-linear potentials, applicable to both elliptic and parabolic equations.

Findings

Gradient bounds for p-Laplace equations using Wolff potentials

Extension of bounds to parabolic equations with caloric potentials

Unified approach for elliptic and parabolic PDE gradient estimates

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.