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

Non convex homogenization problems for singular structures

Andrea Braides 1, and  Valeria Chiadò Piat 2,

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.
Keywords: Singular structures, Homogenization theory, $\Gamma$-convergence.
Mathematics Subject Classification: Primary: 74Q15, 49J45; Secondary: 35B2.
Citation: Andrea Braides, Valeria Chiadò Piat. Non convex homogenization problems for singular structures. Networks and Heterogeneous Media, 2008, 3 (3) : 489-508. doi: 10.3934/nhm.2008.3.489
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