Homogenization of a quasi-linear problem with quadratic growth in perforated domains: An example
type: Item
instance of: scholarly article
title: Homogenization of a quasi-linear problem with quadratic growth in perforated domains: An example
zbMATH Open document ID: 0942.35051
DOI: 10.1016/S0294-1449(97)80129-1
author: Juan Casado-Díaz
published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire
publication date: 1997-11-10T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/78424
review text: This paper is related to the homogenization of a Dirichlet problem. A perturbation of the Laplace operator is considered for a series of domains which varies arbitrarily. As consequence, a new nonlinear term appears in the homogenized problem. A comparison is made with the well known result of \textit{D. Cioranescu} and \textit{F. Murat} [Res. Notes. Math. 60, 98-138 (1982; Zbl 0496.35030)]. To obtain the result, a changement of the unknown function is made and the solution of the linear problem is used to pass to the limit. A Borel measure is also defined by using the limit of the solution of a particular Dirichlet problem. In the last part a corrector result is given and a comparison is made with the case of oscillating coefficients.
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 35B27
Mathematics Subject Classification ID: 35B40
zbMATH DE Number: 1080028
zbMATH Keywords: homogenization
zbMATH Keywords: Laplace operator
zbMATH Keywords: Dirichlet problem
reviewed by: Gelu Paşa
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1080028