Convergence rates and Hölder estimates in almost-periodic homogenization of elliptic systems

Zhongwei Shen

doi:10.2140/apde.2015.8.1565

Convergence rates and Hölder estimates in almost-periodic homogenization of elliptic systems

Zhongwei Shen

Research output: Contribution to journal › Article › peer-review

27 Scopus citations

Abstract

For a family of second-order elliptic systems in divergence form with rapidly oscillating, almost-periodic coefficients, we obtain estimates for approximate correctors in terms of a function that quantifies the almost periodicity of the coefficients. The results are used to investigate the problem of convergence rates. We also establish uniform Hölder estimates for the Dirichlet problem in a bounded C^1,α domain.

Original language	English
Pages (from-to)	1565-1601
Number of pages	37
Journal	Analysis and PDE
Volume	8
Issue number	7
DOIs	https://doi.org/10.2140/apde.2015.8.1565
State	Published - 2015

Bibliographical note

Publisher Copyright:
© 2015 Mathematical Sciences Publishers.

Keywords

almost periodic coefficients
approximate correctors
convergence rates
homogenization

ASJC Scopus subject areas

Analysis
Numerical Analysis
Applied Mathematics

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10.2140/apde.2015.8.1565

Cite this

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abstract = "For a family of second-order elliptic systems in divergence form with rapidly oscillating, almost-periodic coefficients, we obtain estimates for approximate correctors in terms of a function that quantifies the almost periodicity of the coefficients. The results are used to investigate the problem of convergence rates. We also establish uniform H{\"o}lder estimates for the Dirichlet problem in a bounded C1,α domain.",

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AB - For a family of second-order elliptic systems in divergence form with rapidly oscillating, almost-periodic coefficients, we obtain estimates for approximate correctors in terms of a function that quantifies the almost periodicity of the coefficients. The results are used to investigate the problem of convergence rates. We also establish uniform Hölder estimates for the Dirichlet problem in a bounded C1,α domain.

KW - almost periodic coefficients

KW - approximate correctors

KW - convergence rates

KW - homogenization

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JO - Analysis and PDE

JF - Analysis and PDE

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ER -

Convergence rates and Hölder estimates in almost-periodic homogenization of elliptic systems

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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