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March 3, 2026Proceedings of the Royal Society of Edinburgh Section A Mathematics0 citationsOpen Access

First-order homogenization

RCRiccardo CristoferiLDLorenza D’Elia

Key Points

  • Identifying the explicit form of the limiting functional is crucial for understanding energy scaling.
  • The scaling of energy directly relates to the behavior of first-order correctors in the study.
  • Using dual correspondence enhances insights into the relationship between quadratic functionals and PDEs.
  • The refinement of the Riemann–Lebesgue lemma opens new avenues for future mathematical explorations.

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.

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Cite This Study

Cristoferi et al. (2026) studied this question.

synapsesocial.com/papers/69a75bc3c6e9836116a23b3ehttps://doi.org/10.1017/prm.2026.10125
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