Lorentz gradient estimates for a class of elliptic p-Laplacian equations with a Schr\"odinger term

TL;DR

This paper establishes global Lorentz estimates for the gradient of weak solutions to p-Laplace elliptic equations with Schr"odinger potentials, using harmonic analysis techniques to handle degenerate and non-degenerate cases.

Contribution

It introduces a novel approach based on level-set inequalities to derive Lorentz estimates for a broad class of p-Laplace equations with Schr"odinger terms.

Findings

Established Lorentz estimates for gradient of solutions

Unified treatment of degenerate and non-degenerate cases

Applied harmonic analysis techniques to elliptic PDEs

Abstract

We prove in this paper the global Lorentz estimate in term of fractional-maximal function for gradient of weak solutions to a class of p-Laplace elliptic equations containing a non-negative Schr\"odinger potential which belongs to reverse H\"older classes. In particular, this class of p-Laplace operator includes both degenerate and non-degenerate cases. The interesting idea is to use an efficient approach based on the level-set inequality related to the distribution function in harmonic analysis.