Periodic homogenization of integral energies under space-dependent differential constraints
type: Item
instance of: scholarly article
title: Periodic homogenization of integral energies under space-dependent differential constraints
zbMATH Open document ID: 1354.49024
DOI: 10.4171/PM/1988
author: Elisa Davoli
author: Irene Fonseca
published in: Portugaliae Mathematica. Nova Série
publication date: 2016-12-30T00:00:00Z
review text: Summary: A homogenization result for a family of oscillating integral energies \[ u_{\varepsilon}\mapsto\int_{\Omega}f\left(x,\frac x\varepsilon,u_\varepsilon(x)\right)dx,\quad\varepsilon\to0^+ \] is presented, where the fields \(u_{\varepsilon}\) are subjected to first order linear differential constraints depending on the space variable \(x\). The work is based on the theory of \(\mathcal{A}\)-quasiconvexity with variable coefficients and on two-scale convergence techniques, and generalizes the previously obtained results in the case in which the differential constraints are imposed by means of a linear first order differential operator with constant coefficients. The identification of the relaxed energy in the framework of \(\mathcal{A}\)-quasiconvexity with variable coefficients is also recovered as a corollary of the homogenization result.
Mathematics Subject Classification ID: 49J45
Mathematics Subject Classification ID: 35D99
Mathematics Subject Classification ID: 49K20
zbMATH DE Number: 6669854
zbMATH Keywords: homogenization
zbMATH Keywords: two-scale convergence
zbMATH Keywords: \(\mathcal{A}\)-quasiconvexity
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4171/pm/1988
OpenAlex ID: W2557949584
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description: scientific article; zbMATH DE number 6669854