H\"older regularity for degenerate parabolic double-phase equations

TL;DR

This paper establishes local Hölder continuity for solutions to degenerate parabolic double-phase equations, using phase analysis to connect the behavior to p-Laplace or q-Laplace equations.

Contribution

It introduces a phase analysis approach to prove Hölder regularity for solutions of double-phase equations, bridging the gap between p- and q-Laplace behaviors.

Findings

Solutions are locally Hölder continuous.

Phase analysis distinguishes between p- and q-Laplace regimes.

Method extends regularity results to degenerate parabolic double-phase equations.

Abstract

We prove that bounded weak solutions to degenerate parabolic double-phase equations of $p$-Laplace type are locally H\"older continuous. The proof is based on phase analysis and methods for the $p$-Laplace equation. In particular, the phase analysis determines whether the double-phase equation is locally similar to the $p$-Laplace or the $q$-Laplace equation.