{
  "id": "1401.5717",
  "version": "v1",
  "published": "2014-01-22T16:15:05.000Z",
  "updated": "2014-01-22T16:15:05.000Z",
  "title": "Relaxation and integral representation for functionals of linear growth on metric measure spaces",
  "authors": [
    "Heikki Hakkarainen",
    "Juha Kinnunen",
    "Panu Lahti",
    "Pekka Lehtelä"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "This article studies an integral representation of functionals of linear growth on metric measure spaces with a doubling measure and a Poincar\\'e inequality. Such a functional is defined through relaxation, and it defines a Radon measure on the space. For the singular part of the functional, we get the expected integral representation with respect to the variation measure. A new feature is that in the representation for the absolutely continuous part, a constant appears already in the weighted Euclidean case. As an application we show that in a variational minimization problem related to the functional, boundary values can be presented as a penalty term.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-01-22T16:15:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "49Q20",
      "30L99",
      "26B30"
    ],
    "keywords": [
      "metric measure spaces",
      "linear growth",
      "functional",
      "relaxation",
      "variational minimization problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1401.5717H"
    }
  }
}