Abstract
We carry out a comprehensive study of quantitative homogenization of second-order elliptic systems with bounded measurable coefficients that are almost-periodic in the sense of H. Weyl. We obtain uniform local L2 estimates for approximate correctors in terms of a function that quantifies the almost-periodicity of the coefficient matrix. We give a condition that implies the existence of (true) correctors. These estimates as well as similar estimates for the dual approximate correctors yield optimal or near optimal convergence rates in H1 and L2. The L2-based Hölder and Lipschitz estimates at large scale are also established.
Original language | English |
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Pages (from-to) | 187-238 |
Number of pages | 52 |
Journal | Journal des Mathematiques Pures et Appliquees |
Volume | 110 |
DOIs | |
State | Published - Feb 2018 |
Bibliographical note
Publisher Copyright:© 2017 Elsevier Masson SAS
Keywords
- Almost periodic
- Approximate correctors
- Convergence rates
- Homogenization
ASJC Scopus subject areas
- Mathematics (all)
- Applied Mathematics