Riesz potentials and nonlinear parabolic equations

TL;DR

This paper demonstrates that the spatial gradient of solutions to nonlinear degenerate parabolic equations can be estimated using caloric Riesz potentials, extending heat kernel estimates to nonlinear contexts.

Contribution

It establishes pointwise gradient estimates for nonlinear parabolic equations using Riesz potentials, generalizing classical heat equation results.

Findings

Gradient estimates via Riesz potentials are valid for nonlinear degenerate parabolic equations.

Heat kernel type estimates are preserved in the nonlinear setting.

Abstract

The spatial gradient of solutions to nonlinear degenerate parabolic equations can be pointwise estimated by the caloric Riesz potential of the right hand side datum, exactly as in the case of the heat equation. Heat kernels type estimates persist in the nonlinear case