Gradient estimates for an orthotropic nonlinear diffusion equation

TL;DR

This paper establishes that solutions to a specific orthotropic nonlinear diffusion equation are locally Lipschitz continuous in space, providing important regularity results for this class of degenerate parabolic equations.

Contribution

It proves local Lipschitz regularity for solutions to an orthotropic p-Laplacian driven parabolic equation, a novel regularity result for this type of degenerate PDE.

Findings

Solutions are locally Lipschitz continuous in space.

Regularity holds uniformly in time.

Advances understanding of degenerate parabolic equations.

Abstract

We consider a quasilinear degenerate parabolic equation driven by the orthotropic $p-$Laplacian. We prove that local weak solutions are locally Lipschitz continuous in the spatial variable, uniformly in time.