Random homogenization of an obstacle problem
type: Item
instance of: scholarly article
title: Random homogenization of an obstacle problem
zbMATH Open document ID: 1180.35069
author: Luis Caffarelli
author: Antoine Mellet
published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire
publication date: 2009-04-16T00:00:00Z
full work available at URL: https://eudml.org/doc/78847
review text: This paper is devoted to the homogenization process of the obstacle problem associated to a perforated domain in the case when the holes are contained in a set of periodically distributed balls of critical size in the sense of [\textit{D. Cioranescu} and \textit{F. Murat}, Prog. Nonlinear Differ. Equ. Appl. 31, 45--93 (1997; Zbl 0912.35020)]. While the shape of the holes remains unspecified, the rescaled (with respect to the size of the periodic cell) capacity of every hole is assumed to be given by a stationary ergodic process. In order to prove the convergence result, the authors introduce an auxiliary obstacle problem and appropriately construct a fine corrector.
Mathematics Subject Classification ID: 35B27
Mathematics Subject Classification ID: 49J40
Mathematics Subject Classification ID: 47A35
zbMATH DE Number: 5544192
zbMATH Keywords: stationary ergodic process
zbMATH Keywords: auxiliary obstacle problem
reviewed by: Dan Polisevski
MaRDI profile type: Publication
OpenAlex ID: W2067086369
cites work: Ergodic theorems for superadditive processes.
cites work: On convergence of functionals with unilateral constraints
cites work: Homogenization of fully nonlinear, uniformly elliptic and parabolic partial differential equations in stationary ergodic media
cites work: Q3961204
cites work: Gamma-limits of obstacles
cites work: Q3704673
cites work: Q4751270
DOI: 10.1016/J.ANIHPC.2007.09.001
description: scientific article; zbMATH DE number 5544192