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2017 Boundary estimates in elliptic homogenization
Zhongwei Shen
Anal. PDE 10(3): 653-694 (2017). DOI: 10.2140/apde.2017.10.653

Abstract

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 C1,α domains. The Cα , W1,p , and Lp estimates in C1 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 O(ε) error estimates in Lq(Ω) for q = 2d(d 1) and a Lipschitz domain Ω, with no smoothness assumption on the coefficients.

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Zhongwei Shen. "Boundary estimates in elliptic homogenization." Anal. PDE 10 (3) 653 - 694, 2017. https://doi.org/10.2140/apde.2017.10.653

Information

Received: 9 August 2016; Revised: 21 November 2016; Accepted: 22 January 2017; Published: 2017
First available in Project Euclid: 16 November 2017

zbMATH: 1368.35028
MathSciNet: MR3641883
Digital Object Identifier: 10.2140/apde.2017.10.653

Subjects:
Primary: 35B27, 35J55
Secondary: 74B05

Rights: Copyright © 2017 Mathematical Sciences Publishers

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Vol.10 • No. 3 • 2017
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