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 \partial_t(|u|^{q-1}u) - \Delta_p u=0,\quad p>2,\, 0<q<p-1. 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.

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