{
  "id": "2201.11044",
  "version": "v1",
  "published": "2022-01-26T16:34:43.000Z",
  "updated": "2022-01-26T16:34:43.000Z",
  "title": "Partial regularity for $BV$ $ω$-minimizers of quasiconvex functionals",
  "authors": [
    "Zhuolin Li"
  ],
  "comment": "33pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We establish the partial regularity for the $\\omega$-minimizers in $BV$ of variational functionals with strongly quasiconvex integrands of linear growth. The partial regularity of the derivative is established when $\\omega$ satisfies some Dini-type condition. Removing this assumption and only assuming the smallness of $\\omega$ near the origin, we managed to show the partial H\\\"{o}lder continuity of the $\\omega$-minimizers themselves with a normalised excess.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-01-26T16:34:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J47",
      "35J50",
      "49N60"
    ],
    "keywords": [
      "partial regularity",
      "quasiconvex functionals",
      "minimizers",
      "strongly quasiconvex integrands",
      "dini-type condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}