Calculus of Variations and Geometric Measure Theory

L. D'Elia - M. Eleuteri - E. Zappale

Homogenization of supremal functionals in vectorial setting (via power-law approximation)

created by d'elia on 04 Oct 2023

[BibTeX]

preprint

Inserted: 4 oct 2023
Last Updated: 4 oct 2023

Year: 2023

ArXiv: 2310.01175 PDF

Abstract:

We propose a homogenized supremal functional rigorously derived via power-law approximation by functionals of the type ${\rm esssup} f\left(\frac{x}{\varepsilon}, Du\right)$, when $\Omega$ is a bounded open set of $\mathbb R^n$ and $u\in W^{1,\infty}(\Omega;\mathbb R^d)$. The homogenized functional is also deduced directly in the case where the sublevel sets of $f(x,\cdot)$ satisfy suitable convexity properties, as a corollary of homogenization results dealing with pointwise gradient constrained integral functionals.