{
  "abstract": "We derive the $Γ$-limit of convolution-type and discrete energies subject to Dirichlet boundary conditions on periodically perforated domains at the critical exponent. We assume that the length-scale of the non-local interactions is much smaller than the side-length of the cubic perforations and prove that a separation of scales occurs. Exploiting the analogies between the variational frameworks of our interest, we employ a unified argument to overcome the technical difficulties that arise from the scaling invariance of the energies. Our multiscale analysis yields a novel observation that is not related to the non-local nature of the functionals, but rather to the analysis at the critical exponent: we prove that the energy density of the $\\textit{strange term}$ is convex, even in the vector-valued setting.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.11371",
  "author_total": 2,
  "authors": [
    {
      "name": "Giuseppe Cosma Brusca"
    },
    {
      "name": "Giuliana Fusco"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8xmg9vjj2k0m8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.11371",
  "fulltext_url": null,
  "id": "8xmg9vjj2k0m8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.11371",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "1703|Advanced Mathematical Modeling in Engineering"
    ]
  ],
  "openalex": "W7212283652",
  "pdf_url": "https://arxiv.org/pdf/2609.11371",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8xmg9vjj2k0m8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:30Z",
      "native_id": "2609.11371",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.11371"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Emergence of a convex strange term via homogenization of non-local energies at the critical exponent",
  "title_text": "Emergence of a convex strange term via homogenization of non-local energies at the critical exponent",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:30Z",
  "url": "https://research.draconitic.com/paper/8xmg9vjj2k0m8",
  "venue": "arXiv",
  "versions": []
}