Reiterated homogenization of the vector potential formulation of a magnetostatic problem in anisotropic composite media

Abstract

We present an explicit characterization of the effective coefficients of a family of boundary value problems with multiscale periodic oscillatory coefficients, which correspond to the vector potential formulation of a magnetostatic problem in anisotropic composite media with periodic microstructures. Moreover, we study the Γ -convergence of sequences of multiscale periodic integral functionals depending on the curl of divergence-free fields applying the properties of multiscale Young measures associated with sequences of divergence-free fields.