# On the boundary H\"{o}lder regularity for the infinity Laplace equation

## TL;DR

This paper establishes boundary Hölder regularity for the infinity Laplace equation under a broad geometric condition, extending previous results to various domain types using maximum principles and scaling invariance.

## Contribution

It introduces a general geometric condition ensuring boundary Hölder regularity for the infinity Laplace equation, encompassing several classical domain types.

## Key findings

- Boundary Hölder regularity proven under general geometric conditions
- Applicable to exterior cone, Reifenberg flat, and corkscrew domains
- Utilizes maximum principle and scaling invariance techniques

## Abstract

In this note, we prove the boundary H\"{o}lder regularity for the infinity Laplace equation under a proper geometric condition. This geometric condition is quite general, and the exterior cone condition, the Reifenberg flat domains, and the corkscrew domains (including the non-tangentially accessible domains) are special cases. The key idea, following [3], is that the strong maximum principle and the scaling invariance imply the boundary H\"{o}lder regularity.