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
Aalto University
CNRS UMR 5669, 'Unité de Mathématiques Pures et Appliquées' and project-team Inria NUMED, Ecole Normale Supérieure de Lyon
Univ. Bordeaux

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

22 Citations (Scopus)

Résumé

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.

langue originale	Anglais
Pages (de - à)	695-741
Nombre de pages	47
journal	Archive for Rational Mechanics and Analysis
Volume	226
Numéro de publication	2
Les DOIs	https://doi.org/10.1007/s00205-017-1142-z
état	Publié - 1 nov. 2017
Modification externe	Oui

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10.1007/s00205-017-1142-z

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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",

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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

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