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arXiv · 2005.03281

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

Thanh-Nhan Nguyen·Minh-Phuong Tran
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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.

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Thanh-Nhan Nguyen, Minh-Phuong Tran. 2020-05-07. Lorentz estimates for quasi-linear elliptic double obstacle problems involving a Schr\"odinger term. https://doi.org/10.1002/mma.7173

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