{
  "id": "1605.00035",
  "version": "v1",
  "published": "2016-04-29T22:25:04.000Z",
  "updated": "2016-04-29T22:25:04.000Z",
  "title": "Special cases of the planar least gradient problem",
  "authors": [
    "Wojciech Górny",
    "Piotr Rybka",
    "Ahmad Sabra"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We study two special cases of the planar least gradient problem. In the first one, the boundary conditions are imposed on a part of the strictly convex domain. In the second case, we impose the Dirichlet data on the boundary of a rectangle, an example of convex but not strictly convex domain. We show the existence of solutions and study their properties for particular cases of data.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-04-29T22:25:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "gradient problem",
      "special cases",
      "strictly convex domain",
      "boundary conditions",
      "second case"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160500035G"
    }
  }
}