The Cauchy-Dirichlet problem for a general class of parabolic equations

TL;DR

This paper establishes regularity results for a broad class of parabolic equations related to the evolutionary p-Laplacian, using a novel viscosity-type regularization technique.

Contribution

It extends regularity theory to a wide class of parabolic equations inspired by the p-Laplacian, introducing a new viscosity-type regularization method.

Findings

Proved interior Lipschitz regularity.

Established boundary continuity.

Extended regularity results to a broad class of equations.

Abstract

We prove regularity results such as interior Lipschitz regularity and boundary continuity for the Cauchy-Dirichlet problem associated to a class of parabolic equations inspired by the evolutionary $p$-Laplacian, but extending it at a wide scale. We employ a regularization technique of viscosity-type that we find interesting in itself.