# A Boundary Estimate for Singular Parabolic Diffusion Equations

## TL;DR

This paper establishes a boundary modulus of continuity estimate for weak solutions to singular parabolic p-Laplacian equations, using a Wiener-type integral involving elliptic p-capacity, advancing understanding of boundary regularity.

## Contribution

It introduces a new boundary estimate for singular parabolic equations of p-Laplacian type based on a Wiener-type integral, linking boundary behavior to elliptic p-capacity.

## Key findings

- Boundary modulus of continuity estimate proved
- Estimate expressed via Wiener-type integral and p-capacity
- Advances boundary regularity theory for singular 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 singular parabolic equations of p-laplacian type. The estimate is given in terms of a Wiener-type integral, defined by a proper elliptic p-capacity.