Electronic Journal of Differential Equations,
Vol. 2019 (2019), No. 109, pp. 1-29.

Title: Variable Lorentz estimate for generalized Stokes systems in non-smooth domains

Authors: Shuang Liang   (Beijing Jiaotong Univ., Beijing, China)
         Shenzhou Zheng (Beijing Jiaotong Univ., Beijing, China)
         Zhaosheng Feng (Univ. of Texas Rio Grande Valley, Edinburg, TX, USA)

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.