Variable Lorentz estimate for conormal derivative problems of stationary Stokes system with partially BMO coefficients

Abstract

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