{
  "id": "1801.04591",
  "version": "v1",
  "published": "2018-01-14T17:59:54.000Z",
  "updated": "2018-01-14T17:59:54.000Z",
  "title": "On the shape factor of interaction laws for a non-local approximation of the Sobolev norm and the total variation",
  "authors": [
    "Clara Antonucci",
    "Massimo Gobbino",
    "Matteo Migliorini",
    "Nicola Picenni"
  ],
  "comment": "Compte-rendu that summarizes the strategy developed in ArXiv:1708.01231 and ArXiv:1712.04413",
  "categories": [
    "math.FA",
    "math.OC"
  ],
  "abstract": "We consider the family of non-local and non-convex functionals introduced by H. Brezis and H.-M. Nguyen in a recent paper. These functionals Gamma-converge to a multiple of the Sobolev norm or the total variation, depending on a summability exponent, but the exact values of the constants are unknown in many cases. We describe a new approach to the Gamma-convergence result that leads in some special cases to the exact value of the constants, and to the existence of smooth recovery families.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-14T17:59:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26B30",
      "46E35"
    ],
    "keywords": [
      "total variation",
      "sobolev norm",
      "shape factor",
      "interaction laws",
      "non-local approximation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}