A perturbative approach to H\"older continuity of solutions to a nonlocal $p$-parabolic equation

Abstract

We study local boundedness and H\"older continuity of a parabolic equation involving the fractional $p$-Laplacian of order $s$, with $0<s<1$, $2\leq p < \infty$, with a general right hand side. We focus on obtaining precise H\"older continuity estimates. The proof is based on a perturbative argument using the already known H\"older continuity estimate for solutions to the equation with zero right hand side.