{
  "id": "1904.11348",
  "version": "v1",
  "published": "2019-04-24T07:54:19.000Z",
  "updated": "2019-04-24T07:54:19.000Z",
  "title": "$L^p$ regularity of least gradient functions",
  "authors": [
    "Wojciech Górny"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:1811.11138",
  "categories": [
    "math.AP"
  ],
  "abstract": "It is shown that solutions to the anisotropic least gradient problem for boundary data $f \\in L^p(\\partial\\Omega)$ lie in $L^{\\frac{Np}{N-1}}(\\Omega)$; the exponent is shown to be optimal. Moreover, the solutions are shown to be locally bounded with explicit bounds on the rate of blow-up of the solution near the boundary in two settings: in the anisotropic case on the plane and in the isotropic case in any dimension.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-04-24T07:54:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J20",
      "35J25",
      "35J75",
      "35J92"
    ],
    "keywords": [
      "gradient functions",
      "regularity",
      "explicit bounds",
      "gradient problem",
      "anisotropic case"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}