First-order homogenization
Analysis of PDEs
2026-02-04 v1
Abstract
We provide a first-order homogenization result for quadratic functionals. In particular, we identify the scaling of the energy and the explicit form of the limiting functional in terms of the first-order correctors. The main novelty of the paper is the use of the dual correspondence between quadratic functionals and PDEs, combined with a refinement of the classical Riemann-Lebesgue Lemma.
Cite
@article{arxiv.2505.18848,
title = {First-order homogenization},
author = {Riccardo Cristoferi and Lorenza D'Elia},
journal= {arXiv preprint arXiv:2505.18848},
year = {2026}
}