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

Abstract

We propose a homogenized supremal functional rigorously derived via Lp-approximation by functionals of the type ess-supx∈Ω f(x/ϵ, 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.