Lorentz estimates for quasi-linear elliptic double obstacle problems involving a Schrodinger term

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 Schrodinger 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 Calderon-Zygmund theory for nonlinear Schrodinger type equations and variational inequalities for double obstacle problems.