# American Institute of Mathematical Sciences

September  2008, 3(3): 489-508. doi: 10.3934/nhm.2008.3.489

## Non convex homogenization problems for singular structures

 1 Dipartimento di Matematica, Università di Roma 'Tor Vergata', via della Ricerca Scientifica, 00133 Roma 2 Department of mathematical sciences, Politecnico, Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy

Received  March 2008 Published  June 2008

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.
Citation: Andrea Braides, Valeria Chiadò Piat. Non convex homogenization problems for singular structures. Networks & Heterogeneous Media, 2008, 3 (3) : 489-508. doi: 10.3934/nhm.2008.3.489
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