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

TL;DR

This paper establishes precise H"older continuity estimates for solutions to a fractional p-parabolic equation using a perturbative approach based on known estimates for the homogeneous case.

Contribution

It introduces a perturbative method to derive H"older continuity for nonlocal p-parabolic equations with general right hand sides, extending existing results.

Findings

Proves local boundedness and H"older continuity of solutions.

Provides explicit H"older continuity estimates.

Extends known results to equations with non-zero right hand side.

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.