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

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.