A sharp estimate a la calderon-zygmund for the p--laplacian

TL;DR

This paper establishes a higher differentiability result for local weak solutions of the p-Laplace Poisson equation, under sharp conditions on the right-hand side, providing a local scaling invariant a priori estimate.

Contribution

It introduces a new higher differentiability theorem for p-Laplace equations with optimal conditions on the data.

Findings

Higher differentiability under sharp conditions

Scaling invariant a priori estimates

Improved understanding of p-Laplace solutions

Abstract

We consider local weak solutions of the Poisson equation for the p--Laplace operator. We prove a higher differentiability result, under an essentially sharp condition on the right-hand side. The result comes with a local scaling invariant a priori estimate.