Continuity of weak solutions to rough infinitely degenerate equations

TL;DR

This paper extends the DeGiorgi Lemma to infinitely degenerate equations, providing a simpler proof of weak solution continuity that aligns with previous Moser iteration results but applies to homogeneous cases.

Contribution

It generalizes the DeGiorgi Lemma for infinitely degenerate equations and offers a more transparent proof of weak solution continuity for homogeneous equations.

Findings

Established continuity of weak solutions for a class of infinitely degenerate equations

Provided a less technical proof compared to previous methods

Reproduced known results in a more transparent manner

Abstract

We obtain a generalization of the DeGiorgi Lemma to the infinitely degenerate regime and apply it to obtain continuity of weak solutions to certain infinitely degenerate equations. This reproduces the continuity result obtained in arXiv:1506.09203 via Moser iteration, but only for homogeneous equations. However, the proofs are much less technical and more transparent.