{
  "id": "2410.17829",
  "version": "v1",
  "published": "2024-10-23T12:46:44.000Z",
  "updated": "2024-10-23T12:46:44.000Z",
  "title": "Second-order asymptotics of fractional Gagliardo seminorms as $s\\to1^-$ and convergence of the associated gradient flows",
  "authors": [
    "Andrea Kubin",
    "Valerio Pagliari",
    "Antonio Tribuzio"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the second-order asymptotic expansion of the $s$-fractional Gagliardo seminorm as $s\\to1^-$ in terms of a higher order nonlocal functional. We prove a Mosco-convergence result for the energy functionals and that the $L^2$-gradient flows of the energies converge to the $L^2$-gradient flows of the Mosco-limit.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-10-23T12:46:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "49J45",
      "35R11",
      "35B40",
      "45E10",
      "26A33"
    ],
    "keywords": [
      "fractional gagliardo seminorm",
      "associated gradient flows",
      "higher order nonlocal functional",
      "second-order asymptotic expansion",
      "mosco-convergence result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}