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 |
|---|---|
| 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).
Funding
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).
| Funders | Funder number |
|---|---|
| National Science Foundation Arctic Social Science Program | DMS-0855294 |
| National Natural Science Foundation of China (NSFC) | 11001276 |
Keywords
- Homogenization
- Lipschitz domain
- System of elasticity
ASJC Scopus subject areas
- Analysis