Uniform W^{1,p} Estimates for Systems of Linear Elasticity in a Periodic Medium

Jun Geng; Zhongwei Shen; Liang Song

Uniform W^{1,p} Estimates for Systems of Linear Elasticity in a Periodic Medium

Analysis of PDEs 2011-03-30 v1

Authors: Jun Geng , Zhongwei Shen , Liang Song

Abstract

Let $\mathcal{L}_\epsilon$ be a family of elliptic systems of linear elasticity with rapidly oscillating periodic coefficients. We obtain the uniform $W^{1,p}$ estimate in a Lipschitz domain for solutions to the Dirichlet problem, where $(2n/(n+1)) -\delta<p<(2n/(n-1))+\delta$ . The ranges of $p$ 's are sharp for $n=2$ or 3.

Keywords

linear elasticity uniform W^{1,p} estimates periodic coefficients homogenization Lipschitz domain

Cite

@article{arxiv.1103.5721,
  title  = {Uniform W^{1,p} Estimates for Systems of Linear Elasticity in a Periodic Medium},
  author = {Jun Geng and Zhongwei Shen and Liang Song},
  journal= {arXiv preprint arXiv:1103.5721},
  year   = {2011}
}

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