A Boundary Estimate for Degenerate Parabolic Diffusion Equations

TL;DR

This paper establishes a boundary regularity estimate for solutions to degenerate parabolic p-Laplacian equations, linking the modulus of continuity at boundary points to a Wiener-type integral involving p-capacity.

Contribution

It introduces a novel boundary estimate for degenerate parabolic equations using a Wiener-type integral based on p-capacity, advancing understanding of boundary behavior.

Findings

Boundary estimate expressed via Wiener-type integral

Connection between boundary regularity and p-capacity

Extension of regularity theory to degenerate parabolic equations

Abstract

We prove an estimate on the modulus of continuity at a boundary point of a cylindrical domain for local weak solutions to degenerate parabolic equations of $p$-laplacian type. The estimate is given in terms of a Wiener-type integral, defined by a proper elliptic $p$-capacity.