Variable lorentz estimate for stationary stokes system with partially BMO coefficients

Shuang Liang; Shenzhou Zheng

doi:10.3934/cpaa.2019129

Article Contents

2019, Volume 18, Issue 6: 2879-2903. Doi: 10.3934/cpaa.2019129

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Variable lorentz estimate for stationary stokes system with partially BMO coefficients

Shuang Liang and
Shenzhou Zheng^,

Department of Mathematics, Beijing Jiaotong University, Beijing 100044, China

^* Corresponding author
^* Corresponding author

Received: November 30, 2017

Revised: November 30, 2018

Published: May 2019

This research was supported by NSFC grant 11371050

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Abstract

We prove a global Calderón-Zygmund type estimate in the framework of Lorentz spaces for a variable power of the gradients of weak solution pair (u,P ) to the Dirichlet problem of stationary Stokes system. It is mainly assumed that the leading coefficients are merely measurable in one spatial variable and have sufficiently small bounded mean oscillation (BMO) seminorm in the other variables, the boundary of underlying domain is Reifenberg flat, and the variable exponents p(x) satisfy the so-called log-Hölder continuity.

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Mathematics Subject Classification: Primary: 35R05, 76D07; Secondary: 76N10.

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