Γ-convergence of multiscale periodic functionals depending on the time-derivative and the curl operator

We study the Γ-convergence of a family of multiscale periodic quadratic integral functionals defined in a product space, whose densities depend on the time-derivative and on the curl of solenoidal fields, through the multiscale convergence in time–space and the multiscale Young measures in time–space associated with relevant sequences of pairs. An explicit representation of the Γ-limit density is given by means of an infinite dimensional minimization problem.