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Anza Hafsa, Omar; Mandallena, Jean-Philippe; Michaille, Gérard

Homogenization of periodic nonconvex integral functionals in terms of Young measures. (English) Zbl 1107.49013

ESAIM, Control Optim. Calc. Var. 12, 35-51 (2006).
Summary: Homogenization of periodic functionals, whose integrands possess possibly multi-well structure, is treated in terms of Young measures. More precisely, we characterize the \(\Gamma\)-limit of sequences of such functionals in the set of Young measures, extending the relaxation theorem of Kinderlehrer and Pedregal. We also make precise the relationship between our homogenized density and the classical one.

Cited in 3 Documents

MSC:

49J45 Methods involving semicontinuity and convergence; relaxation
35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
49Q20 Variational problems in a geometric measure-theoretic setting
74G65 Energy minimization in equilibrium problems in solid mechanics
74Q05 Homogenization in equilibrium problems of solid mechanics
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems

Keywords:

Young measures; homogenization
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References:

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