Local Hölder regularity for nonlocal parabolic $p$-Laplace equations

Abstract

We prove local Hölder regularity for a nonlocal parabolic equations of the form \begin{align*} \partial_t u + \text{P.V.}\int_{\mathbb{R}^N} \frac{|u(x,t)-u(y,t)|^{p-2}(u(x,t)-u(y,t))}{|x-y|^{N+sp}}\,dy=0, \end{align*} for $p\in (1,\infty )$ and $s\in (0,1)$.

Typos corrected and covering argument has been updated