A-Quasiconvexity: Relaxation and Homogenization
SISSA, Trieste, Italy; firstname.lastname@example.org.
2 Department of MathematicalSciences, Carnegie-Mellon University, Pittsburgh, PA, U.S.A.; email@example.com.
3 Dipartimento di Scienze e Tecnologie Avanzate, Università del Piemonte Orientale, Alessandria, Italy; firstname.lastname@example.org.
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: -quasiconvexity / equi-integrability / Young measure / relaxation / Γ-convergence / homogenization.
© EDP Sciences, SMAI, 2000