Compensated compactness for nonlinear homogenization and reduction of dimension
type: Item
instance of: scholarly article
title: Compensated compactness for nonlinear homogenization and reduction of dimension
zbMATH Open document ID: 1072.35028
author: Patrick Courilleau
author: J. Mossino
published in: Calculus of Variations and Partial Differential Equations
publication date: 2004-12-16T00:00:00Z
review text: In this paper the authors study the limit behavior, as \(\varepsilon \rightarrow 0\), of some nonlinear monotone equations in divergence form, in a domain \(\Omega^\varepsilon\), which is thin in some directions (e.g. \(\Omega^\varepsilon\) is a plate or a thin cylinder). After rescaling to a fixed domain the differential equation is transformed into an equation of the same type, but with the differential operator depending, in an opportune manner, by \(\varepsilon\). With particular assumptions on the coefficients and a suitable compensated compactness, the authors prove a closure result, i.e. the limit problem has the same form. This applies in particular to the limit behaviour of nonlinear monotone equations in laminated plates.
Mathematics Subject Classification ID: 35B27
Mathematics Subject Classification ID: 35Q72
Mathematics Subject Classification ID: 74Q05
zbMATH DE Number: 2123243
zbMATH Keywords: thin domains
zbMATH Keywords: rescaling to a fixed domain
zbMATH Keywords: limit problem
zbMATH Keywords: monotone equations
zbMATH Keywords: laminated plates
reviewed by: Marco Codegone
MaRDI profile type: Publication
full work available at URL: s00526-003-0228-7
OpenAlex ID: W2059106687
DOI: 10.1007/S00526-003-0228-7
description: scientific article; zbMATH DE number 2123243