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

Abstract

We propose a homogenized supremal functional rigorously derived via [Formula: see text]-approximation by functionals of the type ess-sup[Formula: see text], when [Formula: see text] is a bounded open set of [Formula: see text] and [Formula: see text]. The homogenized functional is also deduced directly in the case where the sublevel sets of [Formula: see text] satisfy suitable convexity properties, as a corollary of homogenization results dealing with pointwise gradient constrained integral functionals.