{
  "id": "2109.11908",
  "version": "v2",
  "published": "2021-09-24T11:58:19.000Z",
  "updated": "2022-02-12T12:51:55.000Z",
  "title": "Variational solutions to the total variation flow on metric measure spaces",
  "authors": [
    "Vito Buffa",
    "Juha Kinnunen",
    "Cintia Pacchiano Camacho"
  ],
  "categories": [
    "math.AP",
    "math.FA",
    "math.MG"
  ],
  "abstract": "We discuss a purely variational approach to the total variation flow on metric measure spaces with a doubling measure and a Poincar\\'e inequality. We apply the concept of parabolic De Giorgi classes together with upper gradients, Newtonian spaces and functions of bounded variation to prove a necessary and sufficient condition for a variational solution to be continuous at a given point.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2022-02-12T12:51:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "49J27",
      "49J40",
      "49J45",
      "30L99",
      "35A15"
    ],
    "keywords": [
      "total variation flow",
      "metric measure spaces",
      "variational solution",
      "poincare inequality",
      "purely variational approach"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}