## Abstract

Let {Lε} be a family of elliptic systems of linear elasticity with rapidly oscillating periodic coefficients. We obtain the uniform W ^{1,p} estimate {norm of matrix}∇;u _{ε}{norm of matrix} _{p}≤C{norm of matrix}f{norm of matrix} _{p} in a Lipschitz domain Ω in Rn for solutions to the Dirichlet problem: Lε(uε)=div(f) in Ω and u _{ε}=0 on ∂Ω, where |1p-12|<12n+δ and C, δ>0 are constants independent of ε>0. The ranges are sharp for n=2 or 3.

Original language | English |
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Pages (from-to) | 1742-1758 |

Number of pages | 17 |

Journal | Journal of Functional Analysis |

Volume | 262 |

Issue number | 4 |

DOIs | |

State | Published - Feb 15 2012 |

### Bibliographical note

Funding Information:Jun Geng and Zhongwei Shen were supported in part by NSF Grant DMS-0855294. Liang Song was supported in part by NNSF of China (Grant No. 11001276).

## Keywords

- Homogenization
- Lipschitz domain
- System of elasticity

## ASJC Scopus subject areas

- Analysis

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