Quantitative Analysis of Boundary Layers in Periodic Homogenization

Scott Armstrong; Tuomo Kuusi; Jean Christophe Mourrat; Christophe Prange

doi:10.1007/s00205-017-1142-z

Quantitative Analysis of Boundary Layers in Periodic Homogenization

Scott Armstrong, Tuomo Kuusi, Jean Christophe Mourrat, Christophe Prange

Mathematics

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

Abstract

We prove quantitative estimates on the rate of convergence for the oscillating Dirichlet problem in periodic homogenization of divergence-form uniformly elliptic systems. The estimates are optimal in dimensions larger than three and new in every dimension. We also prove a regularity estimate on the homogenized boundary condition.

Original language	English (US)
Pages (from-to)	695-741
Number of pages	47
Journal	Archive for Rational Mechanics and Analysis
Volume	226
Issue number	2
DOIs	https://doi.org/10.1007/s00205-017-1142-z
State	Published - Nov 1 2017

ASJC Scopus subject areas

Analysis
Mathematics (miscellaneous)
Mechanical Engineering

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title = "Quantitative Analysis of Boundary Layers in Periodic Homogenization",

abstract = "We prove quantitative estimates on the rate of convergence for the oscillating Dirichlet problem in periodic homogenization of divergence-form uniformly elliptic systems. The estimates are optimal in dimensions larger than three and new in every dimension. We also prove a regularity estimate on the homogenized boundary condition.",

author = "Scott Armstrong and Tuomo Kuusi and Mourrat, {Jean Christophe} and Christophe Prange",

note = "Publisher Copyright: {\textcopyright} 2017, Springer-Verlag GmbH Germany.",

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doi = "10.1007/s00205-017-1142-z",

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AU - Armstrong, Scott

AU - Kuusi, Tuomo

AU - Mourrat, Jean Christophe

AU - Prange, Christophe

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Y1 - 2017/11/1

N2 - We prove quantitative estimates on the rate of convergence for the oscillating Dirichlet problem in periodic homogenization of divergence-form uniformly elliptic systems. The estimates are optimal in dimensions larger than three and new in every dimension. We also prove a regularity estimate on the homogenized boundary condition.

AB - We prove quantitative estimates on the rate of convergence for the oscillating Dirichlet problem in periodic homogenization of divergence-form uniformly elliptic systems. The estimates are optimal in dimensions larger than three and new in every dimension. We also prove a regularity estimate on the homogenized boundary condition.

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JO - Archive for Rational Mechanics and Analysis

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Quantitative Analysis of Boundary Layers in Periodic Homogenization

Abstract

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