Shuang Liang, Shenzhou Zheng, Zhaosheng Feng
Abstract:
We prove a global Calderon-Zygmund type estimate in the framework of
Lorentz spaces for the variable power of the gradient of weak solution
pair (u,P) to the generalized steady Stokes system over a bounded
non-smooth domain. It is assumed that the leading coefficients satisfy the
small BMO condition, the boundary of domain belongs to Reifenberg flatness,
and the variable exponent p(x) is log-Holder continuous.
Submitted March 2, 2018. Published September 26, 2019.
Math Subject Classifications: 35D30, 35J47, 76D07.
Key Words: Generalized Stokes systems; Lorentz estimates with variable power;
small BMO; Reifenberg flatness; large-M-inequality principle.
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Shuang Liang Department of Mathematics Beijing Jiaotong University Beijing 100044, China email: shuangliang@bjtu.edu.cn |
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Shenzhou Zheng Department of Mathematics Beijing Jiaotong University Beijing 100044, China email: shzhzheng@bjtu.edu.cn |
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Zhaosheng Feng Department of Mathematics University of Texas Rio Grande Valley Edinburg, TX 78539, USA email: zhaosheng.feng@utrgv.edu |
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