Lorentz estimates for quasi-linear elliptic double obstacle problems involving a Schrödinger 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 Schrödinger 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 Calderón-Zygmund theory for nonlinear Schrödinger type equations and variational inequalities for double obstacle problems.

20 pages