Calderón–Zygmund Estimate for Homogenization of Steady State Stokes Systems in Nonsmooth Domains

Abstract

This paper investigates the higher integrability in homogenization theory for a generalized steady state Stokes system in divergence form with discontinuous coefficients in a bounded nonsmooth domain. We obtain a global and uniform Calderon–Zygmund estimate by essentially proving that both the gradient of the weak solution and its associated pressure are as integrable as the nonhomogeneous term under BMO smallness of the rapidly oscillating periodic coefficients and sufficient flatness of the boundary in the Reifenberg sense. The result improves previous works either concerned with nonhomogenization problem or focused on weakening the regularity requirements on both the coefficients and the boundary to the homogenization of such Stokes systems.