| Issue |
ESAIM: COCV
Volume 5, 2000
|
|
|---|---|---|
| Page(s) | 539 - 577 | |
| DOI | https://doi.org/10.1051/cocv:2000121 | |
| Published online | 15 August 2002 | |
A-Quasiconvexity: Relaxation and Homogenization
1
SISSA, Trieste, Italy; braides@sissa.it.
2
Department of MathematicalSciences,
Carnegie-Mellon University, Pittsburgh, PA, U.S.A.; fonseca@andrew.cmu.edu.
3
Dipartimento di Scienze e Tecnologie Avanzate,
Università del Piemonte Orientale,
Alessandria, Italy; leoni@al.unipmn.it.
Received:
16
March
2000
Revised:
26
September
2000
Integral representation of relaxed energies and of
Γ-limits of functionals
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.
Mathematics Subject Classification: 35D99 / 35E99 / 49J45
Key words: 𝓐-quasiconvexity / equi-integrability / Young measure / relaxation / Γ-convergence / homogenization.
© EDP Sciences, SMAI, 2000
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