{
  "id": "2106.05711",
  "version": "v1",
  "published": "2021-06-10T12:51:04.000Z",
  "updated": "2021-06-10T12:51:04.000Z",
  "title": "On the definition of solution to the total variation flow",
  "authors": [
    "Juha Kinnunen",
    "Christoph Scheven"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We show that the notions of weak solution to the total variation flow based on the Anzellotti pairing and the variational inequality coincide under natural assumptions. The key ingredient in the argument is a duality result for the total variation functional, which is based on an approximation of the total variation by area-type functionals.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-10T12:51:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "total variation flow",
      "definition",
      "total variation functional",
      "variational inequality coincide",
      "weak solution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}