{
  "id": "2009.04048",
  "version": "v1",
  "published": "2020-09-09T00:50:45.000Z",
  "updated": "2020-09-09T00:50:45.000Z",
  "title": "Least gradient problem with Dirichlet condition imposed on a part of the boundary",
  "authors": [
    "Wojciech Górny"
  ],
  "comment": "22 pages, 4 figures",
  "categories": [
    "math.AP"
  ],
  "abstract": "We provide an analysis of the least gradient problem in the case when the boundary datum is only imposed on a part of the boundary. First, we give a characterisation of solutions in a general setting using convex duality theory. Then, we discuss the way in which solutions attain their boundary values, structure of solutions and their regularity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-09-09T00:50:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J20",
      "35J25",
      "35J75",
      "35J92"
    ],
    "keywords": [
      "gradient problem",
      "dirichlet condition",
      "convex duality theory",
      "boundary datum",
      "solutions attain"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}