H\"older regularity for 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.