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

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.