Boundary H\"older gradient estimates for parabolic $p$-Laplace type equations

TL;DR

This paper establishes boundary regularity results for viscosity solutions of parabolic p-Laplace equations, demonstrating pointwise and global $C^{1,eta}$ regularity under certain conditions.

Contribution

It provides new boundary regularity estimates for viscosity solutions of parabolic p-Laplace equations, including pointwise and global $C^{1,eta}$ regularity results.

Findings

Boundary pointwise $C^{1,eta}$ regularity established.

Global $C^{1,eta}$ regularity proven.

Results advance understanding of boundary behavior for p-Laplace type equations.

Abstract

In this paper, we study the boundary regularity for viscosity solutions of parabolic $p$-Laplace type equations. In particular, we obtain the boundary pointwise $C^{1,\alpha}$ regularity and global $C^{1,\alpha}$ regularity.