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Reiterated homogenization of the vector potential formulation of a magnetostatic problem in anisotropic composite media. (English) Zbl 1227.35049

Summary: 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 \(\Gamma \)-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.

MSC:

35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
49J45 Methods involving semicontinuity and convergence; relaxation
78M30 Variational methods applied to problems in optics and electromagnetic theory
78M40 Homogenization in optics and electromagnetic theory
35Q61 Maxwell equations
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