{
  "id": "2207.02488",
  "version": "v1",
  "published": "2022-07-06T07:49:11.000Z",
  "updated": "2022-07-06T07:49:11.000Z",
  "title": "A characterization of BV and Sobolev functions via nonlocal functionals in metric spaces",
  "authors": [
    "Panu Lahti",
    "Andrea Pinamonti",
    "Xiaodan Zhou"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "We study a characterization of BV and Sobolev functions via nonlocal functionals in metric spaces equipped with a doubling measure and supporting a Poincar\\'e inequality. Compared with previous works, we consider more general functionals. We also give a counterexample in the case $p=1$ demonstrating that unlike in Euclidean spaces, in metric measure spaces the limit of the nonlocal functions is only comparable, not necessarily equal, to the variation measure $\\| Df\\|(\\Omega)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-07-06T07:49:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E36",
      "26B30"
    ],
    "keywords": [
      "sobolev functions",
      "nonlocal functionals",
      "metric spaces",
      "characterization",
      "metric measure spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}