{
  "abstract": "We study, through a $Γ$-convergence procedure, the asymptotic behaviour of a general class of nonlocal energies defined on functions taking values in a finite set $Y=\\{y_1,\\dots,y_N\\}\\subset\\mathbb R^m$. These energies are written in terms of double integrals accounting for pairwise interactions in an open set $Ω$, weighted by a kernel $K_\\varepsilon$. If the latter is controlled from above and below by suitable non-negative radial kernels with unit mass concentrating at the origin, then, up to subsequences, the $Γ$-limit has domain $BV(Ω;Y)$ and is given by a local surface energy. We show that the locality of the $Γ$-limit is not guaranteed if the concentration of mass fails. For a class of reference energies, we obtain a more explicit representation of the limit energy, also for non-radial kernels, recovering the limits of isotropic and anisotropic fractional perimeters. We also prove a homogenization result for periodic kernels.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.23389",
  "author_total": 3,
  "authors": [
    {
      "name": "Roberto Alicandro"
    },
    {
      "name": "Giuliana Fusco"
    },
    {
      "name": "Chiara Leone"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3xqg8zzncfr8q.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.23389",
  "fulltext_url": null,
  "id": "3xqg8zzncfr8q",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.23389",
  "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"
    ],
    [
      "openalex",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7222942431",
  "pdf_url": "https://arxiv.org/pdf/2610.23389",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3xqg8zzncfr8q.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:37Z",
      "native_id": "2610.23389",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.23389"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Nonlocal-to-local variational limits of energies on partitions",
  "title_text": "Nonlocal-to-local variational limits of energies on partitions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:31Z",
  "url": "https://research.draconitic.com/paper/3xqg8zzncfr8q",
  "venue": "arXiv",
  "versions": []
}