{
  "id": "2310.03550",
  "version": "v1",
  "published": "2023-10-05T14:00:40.000Z",
  "updated": "2023-10-05T14:00:40.000Z",
  "title": "A sharp lower bound for a class of non-local approximations of the total variation",
  "authors": [
    "Panu Lahti"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "We study a class of non-local functionals that was introduced by Brezis et al. (2022), and can be used to characterize functions of bounded variation. We give a new lower bound for the liminf of these functionals, involving the three different parts of the total variation, with sharp coefficients.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-10-05T14:00:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26B30",
      "26A46"
    ],
    "keywords": [
      "sharp lower bound",
      "total variation",
      "non-local approximations",
      "non-local functionals",
      "sharp coefficients"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}