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

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.