Lorentz estimates for quasi-linear elliptic double obstacle problems involving a Schr\"odinger term

Abstract

Our goal in this article is to study the global Lorentz estimates for gradient of weak solutions to $p$-Laplace double obstacle problems involving the Schr\"odinger term: $-\Delta_p u + \mathbb{V}|u|^{p-2}u$ with bound constraints $\psi_1 \le u \le \psi_2$ in non-smooth domains. This problem has its own interest in mathematics, engineering, physics and other branches of science. Our approach makes a novel connection between the study of Calder\'on-Zygmund theory for nonlinear Schr\"odinger type equations and variational inequalities for double obstacle problems.