{
  "id": "2310.08882",
  "version": "v1",
  "published": "2023-10-13T06:30:41.000Z",
  "updated": "2023-10-13T06:30:41.000Z",
  "title": "BV functions and nonlocal functionals in metric measure spaces",
  "authors": [
    "Panu Lahti",
    "Andrea Pinamonti",
    "Xiaodan Zhou"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:2207.02488",
  "categories": [
    "math.FA"
  ],
  "abstract": "We study the asymptotic behavior of three classes of nonlocal functionals in complete metric spaces equipped with a doubling measure and supporting a Poincar\\'e inequality. We show that the limits of these nonlocal functionals are comparable to the variation $\\| Df\\|(\\Omega)$ or the Sobolev semi-norm $\\int_\\Omega g_f^p\\, d\\mu$, which extends Euclidean results to metric measure spaces. In contrast to the classical setting, we also give an example to show that the limits are not always equal to the corresponding total variation even for Lipschitz functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-10-13T06:30:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E36",
      "26B30"
    ],
    "keywords": [
      "metric measure spaces",
      "nonlocal functionals",
      "bv functions",
      "extends euclidean results",
      "complete metric spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}