Non convex homogenization problems for singular structures

Andrea Braides; Valeria Chiadò Piat

doi:10.3934/nhm.2008.3.489

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

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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

Received: March 2008

Published: September 2008

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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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Mathematics Subject Classification: Primary: 74Q15, 49J45; Secondary: 35B27.

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