A-quasiconvexity: Relaxation and homogenization

Integral representation of relaxed energies and of Gamma -limits of functio nals (u, v) bar right arrow integral (Omega) f(x, u(x), v(x)) dx are obtained when sequences of fields v may develop oscillations and are co nstrained to satisfy a system of first order linear partial differential eq uations. 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 W-1,W-p are recovered.