Multiple Integrals under Differential Constraints: Two-Scale Convergence and Homogenization

Two-scale techniques are developed for sequences of maps {u(k)} subset of L(p) (Omega; R(M)) satisfying a linear differential constraint Au(k) = 0. These, together with F-convergence arguments and using the unfolding operator, provide a homogenization result for energies of the type F(epsilon)(u):= integral(Omega) f (x, x/epsilon, u(x)) dx with u is an element of L(p) (Omega; R(M)), Au = 0, that generalizes current results in the case where A = curl.