Non convex homogenization problems for singular structures

2008, Volume 3, Issue 3: 489-508. doi: 10.3934/nhm.2008.3.489

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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

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.
- Homogenization theory,
- Singular structures,
- $\Gamma$-convergence
Citation: Andrea Braides, Valeria Chiadò Piat. Non convex homogenization problems for singular structures[J]. Networks and Heterogeneous Media, 2008, 3(3): 489-508. doi: 10.3934/nhm.2008.3.489

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Abstract

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.
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