Nonlocal effects in homogenization of \(p_\varepsilon (x)\)-Laplacian in perforated domains
type: Item
instance of: scholarly article
title: Nonlocal effects in homogenization of \(p_\varepsilon (x)\)-Laplacian in perforated domains
zbMATH Open document ID: 1201.35031
author: J. Blot
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2009-07-10T00:00:00Z
review text: The authors deal with the homogenization of a variational problem for a class of nonlinear elliptic equations of \(p_\varepsilon\)-Laplacian with non standard growth conditions. The considered domain has a connected inclusion like a net of infinitely high conductivity. The variational problem is studied in the framework of Sobolev spaces with variable exponents. The sequence of exponents \(p_\varepsilon\) are assumed as an oscillating continuous functions which converges in the uniform metric. The homogenized model, which induces nonlocal effects, is derived. The proof of this result is based on the variational homogenization technique and is illustrated with a periodic example in three dimensional space.
reviewed by: Marco Codegone
Mathematics Subject Classification ID: 35B27
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 74Q05
Mathematics Subject Classification ID: 76M50
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35J92
zbMATH DE Number: 5577471
zbMATH Keywords: variational homogenization
zbMATH Keywords: Sobolev spaces with variable exponents
zbMATH Keywords: nonlocal effects
zbMATH Keywords: net of infinitely high conductivity
MaRDI profile type: Publication
full work available at URL: j.na.2009.02.097
OpenAlex ID: W1996380074
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DOI: 10.1016/J.NA.2009.02.097
description: scientific article; zbMATH DE number 5577471