First-order homogenization

Q: What type of study is this?

This is a Quantitative Study study.

Riccardo Cristoferi; Lorenza D’Elia

doi:10.48550/arxiv.2505.18848

May 24, 2025Open Access

First-order homogenization

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Key Points

The research identifies the scaling of energy in quadratic functionals, indicating new insights into their behavior.
An explicit form of the limiting functional was established, emphasizing the role of the first-order correctors.
The novel approach leverages dual correspondence between quadratic functionals and PDEs, enriching existing theoretical frameworks.
A refinement of the classical Riemann-Lebesgue Lemma was introduced, supporting the findings on energy scaling and functionals.

Implication

This work demonstrates a first-order homogenization in quadratic functionals, suggesting connections to PDEs.

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. (2025) studied this question.

synapsesocial.com/papers/68da58d8c1728099cfd111fe https://doi.org/10.48550/arxiv.2505.18848

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First-order homogenization

Key Points

Implication

Abstract

Discussion

Cite This Study

First-order homogenization

Key Points

Implication

Abstract

Discussion

Cite This Study

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