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.
An integral representation result is obtained for the variational limit of the family functionals Ω f ( x ε , Du)dx, ε > 0, when the integrand f = f (x, v) is a Carathéodory function, periodic in x, convex in v and with nonstandard growth.
Stochastic-periodic homogenization is studied for the Maxwell equations with nonlinear and periodic electric conductivity. It is shown by the stochastic-twoscale convergence method that the sequence of solutions of a class of highly oscillatory problems converges to the solution of a homogenized Maxwell equation.
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