Quantitative stochastic homogenization of convex integral functionals
[Homogénéisation stochastique quantitative de fonctionnelles intégrales convexes]
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 49 (2016) no. 2, pp. 423-481.

Nous présentons des résultats quantitatifs pour l'homogénéisation de fonctionnelles intégrales uniformément convexes avec coefficients aléatoires sous hypothèses d'indépendance. Le résultat principal est une estimation d'erreur pour le problème de Dirichlet qui est algébrique (mais sous-optimale) en la taille de l'erreur, mais optimale en intégrabilité stochastique. Comme application, nous obtenons des estimées C0,1 pour les minimiseurs locaux de telles fonctionnelles d'énergie.

We present quantitative results for the homogenization of uniformly convex integral functionals with random coefficients under independence assumptions. The main result is an error estimate for the Dirichlet problem which is algebraic (but sub-optimal) in the size of the error, but optimal in stochastic integrability. As an application, we obtain quenched C0,1 estimates for local minimizers of such energy functionals.

DOI : 10.24033/asens.2287
Classification : 35B27, 60H25, 35J20, 35J62
Keywords: Stochastic homogenization, error estimates, calculus of variations, quenched Lipschitz estimate.
Mot clés : Homogénéisation stochastique, estimations d'erreur, calcul des variations, estimées Lipschitz. 
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     title = {Quantitative stochastic homogenization of convex integral functionals},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {423--481},
     publisher = {Soci\'et\'e Math\'ematique de France. Tous droits r\'eserv\'es},
     volume = {Ser. 4, 49},
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Armstrong, Scott N.; Smart, Charles K. Quantitative stochastic homogenization of convex integral functionals. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 49 (2016) no. 2, pp. 423-481. doi : 10.24033/asens.2287. http://www.numdam.org/articles/10.24033/asens.2287/

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