Quantitative Analysis of Boundary Layers in Periodic Homogenization

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

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)1-47
Number of pages47
JournalArchive for Rational Mechanics and Analysis
DOIs
StateAccepted/In press - Jun 23 2017

Fingerprint

Periodic Homogenization
Quantitative Analysis
Boundary Layer
Boundary layers
Boundary conditions
Chemical analysis
Estimate
Elliptic Systems
Dirichlet Problem
Divergence
Rate of Convergence
Regularity

ASJC Scopus subject areas

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

Cite this

Quantitative Analysis of Boundary Layers in Periodic Homogenization. / Armstrong, Scott; Kuusi, Tuomo; Mourrat, Jean Christophe; Prange, Christophe.

In: Archive for Rational Mechanics and Analysis, 23.06.2017, p. 1-47.

Research output: Contribution to journalArticle

Armstrong, Scott ; Kuusi, Tuomo ; Mourrat, Jean Christophe ; Prange, Christophe. / Quantitative Analysis of Boundary Layers in Periodic Homogenization. In: Archive for Rational Mechanics and Analysis. 2017 ; pp. 1-47.
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