A-Quasiconvexity: Relaxation and Homogenization
Andrea Braides, Irene Fonseca, Giovanni Leoni · ESAIM Control Optimisation and Calculus of Variations · 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.