{
  "annotation_id": "13c40227-65c9-4aac-a4ab-91e6b5ca4520",
  "date_created": "2026-02-17T05:53:16.032000Z",
  "date_modified": "2026-02-17T05:53:16.032000Z",
  "file_hash": "ecb5f1537781dc675217ec7a74b2bad07fa4a474c2e469155d1d90a298cbb454",
  "private": false,
  "record": {
    "abstract": "We investigate a homogenization problem related to a non-local interface energy with a periodic forcing term. We show the existence of planelike minimizers for such energy. Moreover, we prove that, under suitable assumptions on the non-local kernel and the external field, the sequence of rescaled energies $\\Gamma$-converges to a suitable local anisotropic perimeter, where the anisotropy is defined as the limit of the normalized energy of a planelike minimizer in larger and larger cubes (i.e., what is called in jargon \"stable norm\"). To obtain this, we also establish several auxiliary results, including: the minimality of the level sets of the minimizers, explicit bounds on the oscillations of the minimizers, density estimates for almost minimizers, and non-local perimeter estimates in the large.",
    "arxiv_id": "2601.08677",
    "authors": [
      "Serena Dipierro",
      "Matteo Novaga",
      "Enrico Valdinoci",
      "Riccardo Villa"
    ],
    "categories": [
      "math.AP",
      "math.DS"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "Non-local planelike minimizers and $\\Gamma$-convergence of periodic energies to a local anisotropic perimeter",
    "url": "https://arxiv.org/abs/2601.08677",
    "version": "v2"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "7f308fab-b959-40b0-b491-1ab416e34672",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}