On the Hölder regularity of signed solutions to a doubly nonlinear equation. Part II

Abstract

We demonstrate two proofs for the local Hölder continuity of possibly sign-changing solutions to a class of doubly nonlinear parabolic equations whose prototype is

The first proof takes advantage of the expansion of positivity for the degenerate, parabolic $p$-Laplacian, thus simplifying the argument; the second proof relies solely on the energy estimates for doubly nonlinear parabolic equations. After proper adaptations of the interior arguments, we also obtain the boundary regularity for initial-boundary value problems of Dirichlet and Neumann type.