Homogenization of Stokes Systems and Uniform Regularity Estimates

@article{Gu2015HomogenizationOS,
title={Homogenization of Stokes Systems and Uniform Regularity Estimates},
author={Shu Gu and Zhongwei Shen},
journal={SIAM J. Math. Anal.},
year={2015},
volume={47},
pages={4025-4057}
}
• Published 2015
• Mathematics, Computer Science
• SIAM J. Math. Anal.
• 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
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