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

Université Paris Dauphine
Department of Mathematics and Systems Analysis
Aalto University
CNRS UMR 5669, 'Unité de Mathématiques Pures et Appliquées' and project-team Inria NUMED, Ecole Normale Supérieure de Lyon
Univ. Bordeaux

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

22 Citations (Scopus)

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
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
Publication status	Published - 1 Nov 2017
Externally published	Yes

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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.",

year = "2017",

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

language = "English",

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AU - Kuusi, Tuomo

AU - Mourrat, Jean Christophe

AU - Prange, Christophe

PY - 2017/11/1

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.

U2 - 10.1007/s00205-017-1142-z

DO - 10.1007/s00205-017-1142-z

M3 - Article

AN - SCOPUS:85021209779

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EP - 741

JO - Archive for Rational Mechanics and Analysis

JF - Archive for Rational Mechanics and Analysis

IS - 2

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Quantitative Analysis of Boundary Layers in Periodic Homogenization

Abstract

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