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Lorentz estimates for quasilinear elliptic double obstacle problems involving a Schrödinger term
Mathematical Methods in the Applied Sciences ( IF 2.9 ) Pub Date : 2021-01-20 , DOI: 10.1002/mma.7173
Thanh‐Nhan Nguyen 1 , Minh‐Phuong Tran 2
Affiliation  

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: Δ p u + 𝕍 | u | p 2 u with bound constraints ψ1 ≤ u ≤ ψ2 in nonsmooth 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.

中文翻译:

Lorentz估计涉及Schrödinger项的拟线性椭圆双障碍问题

本文的目标是研究涉及Schrödinger项的p -Laplace双障碍问题的弱解的梯度的全球Lorentz估计: - Δ p ü + 𝕍 | ü | p - 2个 ü 具有结合的约束ψ 1  ≤  ü  ≤  ψ 2在非光滑结构域。这个问题在数学,工程学,物理学和其他科学领域都有自己的兴趣。我们的方法在研究非线性Schrödinger型方程的Calderón-Zygmund理论与双障碍问题的变分不等式之间建立了新颖的联系。
更新日期:2021-01-20
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