On the homogenization of quasilinear divergence structure operators
type: Item
instance of: scholarly article
title: On the homogenization of quasilinear divergence structure operators
zbMATH Open document ID: 0636.35027
DOI: 10.1007/BF01762357
author: N. Fusco
author: Gioconda Moscariello
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 1987-01-01T00:00:00Z
review text: A family of boundary value problems of the type \[ (1)\quad -div a(x/\epsilon,u,Du)=f,\quad u\in H_ 0^{1,p}(\Omega) \] is considered, where a(x,u,\(\epsilon)\) is periodic in x and satisfies suitable growth conditions, \(\epsilon >0\), \(p>1\). It is proved that the solutions \(u_{\epsilon}\) of (1) converge weakly to \(u_ 0\) satisfying \[ -div b(u,Du)=f,\quad u\in H_ 0^{1,r}(\Omega), \] and \(a(x/\epsilon,u_{\epsilon},Du_{\epsilon})\) converge to \(b(u_ 0,Du_ 0)\) weakly in \(L^{p'},p'=p/(p-1)\), where b(u,\(\xi)\) is given by an explicit formula. Moreover, it is shown that certain structure conditions are preserved for the limit operator.
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 35B30
Mathematics Subject Classification ID: 35A35
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 4036285
zbMATH Keywords: second order
zbMATH Keywords: quasilinear
zbMATH Keywords: homogenization
zbMATH Keywords: growth conditions
zbMATH Keywords: explicit formula
zbMATH Keywords: structure
zbMATH Keywords: limit operator
reviewed by: Milan Kučera
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01762357
OpenAlex ID: W1993965252
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description: scientific article; zbMATH DE number 4036285