Homogenization of Stokes Systems and Uniform Regularity Estimates

Abstract

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 $L^{\infty }$ estimates for the pressure as well as a Liouville property for solutions in ${\mathbb{R}}^d$. We also obtain the boundary $W^{1,p}$ estimates in a bounded $C^1$ domain for any $1<p<\infty$.

36 pages; minor revision of the previous version. To appear in the SIAM J. Math. Analysis

References in corpus (1)

• From Small Space to Small Width in Resolution

Cited by in corpus (1)

• Uniform Regularity Estimates in Homogenization Theory of Elliptic System with Lower Order terms