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A-Quasiconvexity: Relaxation and Homogenization

Published online by Cambridge University Press:  15 August 2002

Andrea Braides ,
Irene Fonseca  and
Giovanni Leoni
Andrea Braides
Affiliation:
SISSA, Trieste, Italy; braides@sissa.it.
Irene Fonseca
Affiliation:
Department of MathematicalSciences, Carnegie-Mellon University, Pittsburgh, PA, U.S.A.; fonseca@andrew.cmu.edu.
Giovanni Leoni
Affiliation:
Dipartimento di Scienze e Tecnologie Avanzate, Università del Piemonte Orientale, Alessandria, Italy; leoni@al.unipmn.it.
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Abstract

Integral representation of relaxed energies and of Γ-limits of functionals $$ (u,v)\mapsto \int_\Omega f( x,u(x),v(x))\,dx $$ are obtained when sequences of fields v may develop oscillations and are constrained to satisfy a system of first order linear partial differential equations. This framework includes the treatement of divergence-free fields, Maxwell's equations in micromagnetics, and curl-free fields. In the latter case classical relaxation theorems in W1,p, are recovered.

Keywords

${\cal A}$-quasiconvexityequi-integrabilityYoung measurerelaxationΓ-convergencehomogenization.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 5 , 2000 , pp. 539 - 577
Copyright
© EDP Sciences, SMAI, 2000

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