A note on the proof of H\"older continuity to weak solutions of elliptic equations

TL;DR

This paper discusses a proof of H"older continuity for weak solutions of elliptic equations, utilizing ideas from parabolic theory and combining De Giorgi's and Moser's methods.

Contribution

It introduces a novel approach by borrowing techniques from parabolic theory to enhance the proof of H"older continuity in elliptic equations.

Findings

H"older continuity of weak solutions is established.

A new proof technique combining De Giorgi's and Moser's methods is proposed.

Insights from parabolic theory are effectively applied.

Abstract

By borrowing ideas from the parabolic theory, we use a combination of De Giorgi's and Moser's methods to give some remarks on the proof of H\"older continuity of weak solutions of elliptic equations.