This paper is concerned with uniform regularity estimates for a family of Stokes systems with rapidly oscillating periodic coefficients. We establish interior Lipschitz estimates for the velocity and L∞ estimates for the pressure as well as a Liouville property for solutions in ℝd. We also obtain the boundary W1,p estimates in a bounded C1 domain for any 1 < p < ∞.
Digital Object Identifier (DOI)
Gu, Shu and Shen, Zhongwei, "Homogenization of Stokes Systems and Uniform Regularity Estimates" (2015). Mathematics Faculty Publications. 17.