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Reiterated periodic homogenization of integral functionals with convex and nonstandard growth integrands. (English) Zbl 1469.35023

Summary: Multiscale periodic homogenization is extended to an Orlicz-Sobolev setting. It is shown by the reiteraded periodic two-scale convergence method that the sequence of minimizers of a class of highly oscillatory minimizations problems involving convex functionals, converges to the minimizers of a homogenized problem with a suitable convex function.

MSC:

35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
35B40 Asymptotic behavior of solutions to PDEs
35J20 Variational methods for second-order elliptic equations
35J25 Boundary value problems for second-order elliptic equations
35J62 Quasilinear elliptic equations
46J10 Banach algebras of continuous functions, function algebras
49J45 Methods involving semicontinuity and convergence; relaxation
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