Non convex homogenization problems for singular structures
Andrea Braides, Valeria Chiadò Piat · Networks and Heterogeneous Media · 2008
We prove a homogenization theorem for non-convex functionals depending onvector-valued functions, defined on Sobolev spaces with respect to oscillating measures.The proof combines the use of the localization methods of$\Gamma$-convergence with a 'discretization' argument, which allows tolink the oscillating energies to functionals defined on a single Lebesgue space, and tostate the hypothesis of $p$-connectedness of the underlying periodic measurein a handy way.