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Multiscale periodic homogenization is extended to 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.

Reiterated periodic homogenization of integral functionals with convex and nonstandard growth integrands