Regularity of Solutions to Degenerate Non-Doubling Second Order Equations

TL;DR

This paper proves the continuity of weak solutions to a class of infinitely degenerate quasilinear equations, even when the associated metric is non-doubling, advancing understanding of degenerate PDE regularity.

Contribution

It establishes continuity results for solutions to degenerate equations with non-doubling metrics, a significant extension beyond classical regularity theory.

Findings

Weak solutions are continuous despite degeneracy.

The associated Fefferman-Phong metric may be non-doubling.

Results apply to a broad class of degenerate equations.

Abstract

We prove that every weak solution to a certain class of infinitely degenerate quasilinear equations is continuous. An essential feature of the operators we consider is that their Fefferman-Phong associated metric may be non doubling with respect to Lebesgue measure.