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

We propose a homogenized supremal functional rigorously derived via L p -approximation by functionals of the type ess-sup x ∈ Ω f (x , D u) , when Ω is a bounded open set of ℝ n and u ∈ W 1 , ∞ (Ω ; ℝ d). 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. [ABSTRACT FROM AUTHOR]