Inserted: 16 jun 2007
Last Updated: 8 jul 2008
Journal: Netw. Heterog. Media
Pages: 489 - 508
We prove a homogenization theorem for non-convex functionals depending on vector-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 to link the oscillating energies to functionals defined on a single Lebesgue space, and to state the hypothesis of $p$-connectedness of the underlying periodic measure in a handy way.
Keywords: Homogenization, Singular structures, p-connectedness