Bounded correctors in almost periodic homogenization

Armstrong, Scott; Gloria, Antoine; Kuusi, Tuomo

Type de document :

Article dans une revue scientifique: Article original

DOI :

10.1007/s00205-016-1004-0

Titre :

Bounded correctors in almost periodic homogenization

Auteur(s) :

Armstrong, Scott [Auteur]
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Gloria, Antoine [Auteur]
Quantitative methods for stochastic models in physics [MEPHYSTO]
Département de Mathématique [Bruxelles] [ULB]
Kuusi, Tuomo [Auteur]
Aalto University

Titre de la revue :

Archive for Rational Mechanics and Analysis

Pagination :

393--426

Éditeur :

Springer Verlag

Date de publication :

2016

ISSN :

0003-9527

Discipline(s) HAL :

Mathématiques [math]/Equations aux dérivées partielles [math.AP]

Résumé en anglais : [en]

We show that certain linear elliptic equations (and systems) in divergence form with almost periodic coefficients have bounded, almost periodic correctors. This is proved under a new condition we introduce which quantifies ...
Lire la suite >We show that certain linear elliptic equations (and systems) in divergence form with almost periodic coefficients have bounded, almost periodic correctors. This is proved under a new condition we introduce which quantifies the almost periodic assumption and includes (but is not restricted to) the class of smooth, quasiperiodic coefficient fields which satisfy a Diophantine-type condition previously considered by Kozlov. The proof is based on a quantitative ergodic theorem for almost periodic functions combined with the new regularity theory recently introduced by the first author and Shen for equations with almost periodic coefficients. This yields control on spatial averages of the gradient of the corrector, which is converted into estimates on the size of the corrector itself via a multiscale Poincaré-type inequality.Lire moins >

Langue :

Anglais

Comité de lecture :

Oui

Audience :

Internationale

Vulgarisation :

Non

Projet Européen :

Quantitative methods in stochastic homogenization

Collections :