Analysis & PDE
- Anal. PDE
- Volume 10, Number 3 (2017), 653-694.
Boundary estimates in elliptic homogenization
For a family of systems of linear elasticity with rapidly oscillating periodic coefficients, we establish sharp boundary estimates with either Dirichlet or Neumann conditions, uniform down to the microscopic scale, without smoothness assumptions on the coefficients. Under additional smoothness conditions, these estimates, combined with the corresponding local estimates, lead to the full Rellich-type estimates in Lipschitz domains and Lipschitz estimates in domains. The , , and estimates in domains for systems with VMO coefficients are also studied. The approach is based on certain estimates on convergence rates. As a biproduct, we obtain sharp error estimates in for and a Lipschitz domain , with no smoothness assumption on the coefficients.
Anal. PDE, Volume 10, Number 3 (2017), 653-694.
Received: 9 August 2016
Revised: 21 November 2016
Accepted: 22 January 2017
First available in Project Euclid: 16 November 2017
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Shen, Zhongwei. Boundary estimates in elliptic homogenization. Anal. PDE 10 (2017), no. 3, 653--694. doi:10.2140/apde.2017.10.653. https://projecteuclid.org/euclid.apde/1510843452