{
  "annotation_id": "61aa1a7f-b0d3-4d8c-b20c-2528f01ea2ea",
  "date_created": "2026-02-17T05:53:16.129000Z",
  "date_modified": "2026-02-17T05:53:16.129000Z",
  "file_hash": "5407718196ea50557d8923b93fcfc88ae82449f5db3f09bc036ce6b5fc1de377",
  "private": false,
  "record": {
    "abstract": "Singular perturbations have been used to select solutions of (non-convex) variational problems with a multiplicity of minimizers. The prototype of such an approach is the gradient theory of phase transitions by L. Modica, who specialized some earlier Gamma-convergence results by himself and S. Mortola contained in a seminal paper, validating the so-called minimal-interface criterion. I will give an overview of some recent results on perturbations with fractional and higher-order seminorms both in the framework of phase transitions and of free-discontinuity problems, relating these results with the Bourgain-Brezis-Mironescu and Maz\u0027ya-Shaposhnikova limit analysis for fractional Sobolev seminorms, and with the theory of Gamma-expansions.",
    "arxiv_id": "2601.08573",
    "authors": [
      "Andrea Braides"
    ],
    "categories": [
      "math.AP",
      "math-ph",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "Non-local singular perturbations of non-convex functionals -- recent results",
    "url": "https://arxiv.org/abs/2601.08573",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "94e504c7-b034-4c8f-8704-4d302eba9244",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}