Homogenization of supremal functionals in the vectorial case (via Lp-approximation)

We propose a homogenized supremal functional rigorously derived via Lp -approximation by functionals of the type ess-supx∈Ωf(xε,Du) , when Ω is a bounded open set of Rn and u∈W1,∞(Ω;Rd) . The homogenized functional is also deduced directly in the case where the sublevel sets of f(x,⋅) satisfy suitable convexity properties, as a corollary of homogenization results dealing with pointwise gradient constrained integral functionals.