Nonlinear stochastic homogenization
type: Item
instance of: scholarly article
title: Nonlinear stochastic homogenization
zbMATH Open document ID: 0607.49010
DOI: 10.1007/BF01760826
author: G. Dal Maso
author: Luciano Modica
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 1986-01-01T00:00:00Z
review text: In the framework of calculus of variations, the authors study stochastic homogenization of integral functionals. The integrand is supposed measurable in the first variable and convex in the second one. The main feature of this paper is to pass from the view-point of the stochastic differential equations to be solved to that one of the random integral functionals to be minimized. In order to study the random integral functionals, that are ''measurable'' maps \(\omega\to F(\omega)\) from a probabilistic space \(\Omega\) into the functional class \({\mathcal F}\), and to study their convergence, a topological structure is given on \({\mathcal F}.\) The applications of this result are concerned with a large number of real phenomena in physics, chemistry and engineering, where the structures to be homogenized are not periodic but only stochastically periodic.
Mathematics Subject Classification ID: 49J45
Mathematics Subject Classification ID: 49J55
Mathematics Subject Classification ID: 60H15
Mathematics Subject Classification ID: 49K45
zbMATH DE Number: 3981928
zbMATH Keywords: nonlinear problems
zbMATH Keywords: stochastic homogenization of integral functionals
reviewed by: Marco Codegone
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01760826
OpenAlex ID: W2063773847
description: scientific article; zbMATH DE number 3981928