Periodic homogenization for convex functionals using Mosco convergence

We study the relationship between the Mosco convergence of a sequence of convex proper lower semicontinuous functionals, defined on a reflexive Banach space, and the convergence of their subdifferentiels as maximal monotone graphs. We then apply these results together with the unfolding method (see Cioranescu-Damlamian-Griso, 2002) to study the homogenization of equations of the form $-\textrm{ div }d_\varepsilon=f $, with $(\nabla u_\varepsilon(x),d_\varepsilon(x)) \in \partial \varphi_\varepsilon(x)$ where $\varphi_\varepsilon (x,.)$ is a Carath'eodory convex function with suitable growth and coercivity conditions