# A-Quasiconvexity: Relaxation and Homogenization

Andrea Braides; Irene Fonseca; Giovanni Leoni

ESAIM: Control, Optimisation and Calculus of Variations (2010)

- Volume: 5, page 539-577
- ISSN: 1292-8119

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topBraides, Andrea, Fonseca, Irene, and Leoni, Giovanni. "A-Quasiconvexity: Relaxation and Homogenization." ESAIM: Control, Optimisation and Calculus of Variations 5 (2010): 539-577. <http://eudml.org/doc/197360>.

@article{Braides2010,

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.
},

author = {Braides, Andrea, Fonseca, Irene, Leoni, Giovanni},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {$\{\cal A\}$-quasiconvexity; equi-integrability; Young measure; relaxation; Γ-convergence;
homogenization.; Young measures; Gamma-convergence; differential constraint; integral representation of the relaxed energy},

language = {eng},

month = {3},

pages = {539-577},

publisher = {EDP Sciences},

title = {A-Quasiconvexity: Relaxation and Homogenization},

url = {http://eudml.org/doc/197360},

volume = {5},

year = {2010},

}

TY - JOUR

AU - Braides, Andrea

AU - Fonseca, Irene

AU - Leoni, Giovanni

TI - A-Quasiconvexity: Relaxation and Homogenization

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2010/3//

PB - EDP Sciences

VL - 5

SP - 539

EP - 577

AB -
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.

LA - eng

KW - ${\cal A}$-quasiconvexity; equi-integrability; Young measure; relaxation; Γ-convergence;
homogenization.; Young measures; Gamma-convergence; differential constraint; integral representation of the relaxed energy

UR - http://eudml.org/doc/197360

ER -

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