{
  "id": "1806.02456",
  "version": "v1",
  "published": "2018-06-06T23:15:10.000Z",
  "updated": "2018-06-06T23:15:10.000Z",
  "title": "A local estimate for the total variation flow of curves",
  "authors": [
    "Lorenzo Giacomelli",
    "Michał Łasica"
  ],
  "comment": "7 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "If $\\boldsymbol u \\colon [0, \\infty[\\times I \\to \\mathbb R^n$ is the solution to the total variation flow on an interval $I$ with initial datum $\\boldsymbol u_0 \\in BV(I, \\mathbb R^n)$, then $|\\boldsymbol u_x(t, \\cdot)| \\leq |\\boldsymbol u_{0,x}|$ in the sense of measures on $I$ for $t>0$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-06-06T23:15:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35A23",
      "35K51",
      "35K92"
    ],
    "keywords": [
      "total variation flow",
      "local estimate",
      "initial datum"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}