H\"older continuity for the $p$-Laplace equation using a differential inequality

TL;DR

This paper introduces a novel approach using an ordinary differential inequality to prove H"older continuity of solutions to the p-Laplace equation, offering an alternative to classical iterative methods.

Contribution

The paper presents a new method employing differential inequalities to establish regularity results for p-Laplace solutions, differing from traditional iterative techniques.

Findings

Proves H"older continuity for p-Laplace solutions

Uses differential inequality method instead of classical iteration

Provides an alternative proof technique for regularity

Abstract

We study H\"older continuity for solutions of the $p$-Laplace equation. This is established through a method involving an ordinary differential inequality, in contrast to the classical proof of the De Giorgi-Nash-Moser Theorem which uses iteration of an inequality through concentric balls.