{
  "id": "1103.3365",
  "version": "v1",
  "published": "2011-03-17T09:37:21.000Z",
  "updated": "2011-03-17T09:37:21.000Z",
  "title": "Passing to the limit in maximal slope curves: from a regularized Perona-Malik equation to the total variation flow",
  "authors": [
    "Maria Colombo",
    "Massimo Gobbino"
  ],
  "comment": "19 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We prove that solutions of a mildly regularized Perona-Malik equation converge, in a slow time scale, to solutions of the total variation flow. The convergence result is global-in-time, and holds true in any space dimension. The proof is based on the general principle that \"the limit of gradient-flows is the gradient-flow of the limit\". To this end, we exploit a general result relating the Gamma-limit of a sequence of functionals to the limit of the corresponding maximal slope curves.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-03-17T09:37:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K55",
      "35B40",
      "35K90"
    ],
    "keywords": [
      "total variation flow",
      "corresponding maximal slope curves",
      "mildly regularized perona-malik equation converge",
      "slow time scale"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1103.3365C"
    }
  }
}