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. Analysis},
  year={2015},
  volume={47},
  pages={4025-4057}
}
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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References

Publications referenced by this paper.
SHOWING 1-10 OF 23 REFERENCES

Nonlinear systems of the type of the stationary Navier–Stokes systems

M. Giaquinta, G Modica
  • J. Reine Angew. Math.,
  • 1982
VIEW 3 EXCERPTS
HIGHLY INFLUENTIAL

1,p estimates for elliptic equations with Neumann boundary conditions in Lipschitz domains

W J. Geng
  • Adv. Math.,
  • 2012
VIEW 1 EXCERPT

1,p estimates for elliptic homogenization problems in nonsmooth domains

W Z. Shen
  • Indiana Univ. Math. J.,
  • 2008
VIEW 1 EXCERPT