Homogenization of supremal functionals in the vectorial case (via L^p-approximation)

2023/10/02 by D'Elia, Lorenza, Eleuteri, Michela, Zappale, Elvira · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2310.01175

Abstract

We propose a homogenized supremal functional rigorously derived via L^p-approximation by functionals of the type \undersetx∈Ωess-sup\hspace0.03cm f((x)/(ε), Du), when Ω is a bounded open set of \mathbb Rⁿ and u∈ W^1,∞(Ω;\mathbb 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.

Cited by

• First-order homogenization

Related

• A relaxation result in the vectorial setting and L^p-approximation for L^∞-functionals
• Homogenization of singular integrals in W^1,∞
• The role of intrinsic distances in the relaxation of\n L^\∞-functionals
• Revisited convexity notions for L^∞ variational problems
• Dimension reduction for functionals on solenoidal vector fields