H\"older regularity for the fractional p-Laplacian, revisited

TL;DR

This paper provides an alternative proof for the local H"older regularity of solutions to fractional p-Laplace equations, using clustering and expansion techniques focused on positivity recentering.

Contribution

It introduces a novel proof method for regularity results of fractional p-Laplace equations based on clustering and positivity recentering.

Findings

Establishes local H"older regularity for solutions

Introduces a new proof technique based on clustering

Simplifies understanding of fractional p-Laplace regularity

Abstract

We present an alternative proof for local H\"older regularity of the solutions of the fractional p-Laplace equations, based on clustering and expansion (more precisely, recentering) of positivity.