{
  "id": "2102.13065",
  "version": "v1",
  "published": "2021-02-25T18:25:04.000Z",
  "updated": "2021-02-25T18:25:04.000Z",
  "title": "Maximum principles, Liouville theorem and symmetry results for the fractional $g-$Laplacian",
  "authors": [
    "Sandra Molina",
    "Ariel Salort",
    "Hernán Vivas"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We study different maximum principles for non-local non-linear operators with non-standard growth that arise naturally in the context of fractional Orlicz-Sobolev spaces and whose most notable representative is the fractional $g-$Laplacian: \\[ (-\\Delta_g)^su(x):=\\textrm{p.v.}\\int_{\\mathbb{R}^n}g\\left(\\frac{u(x)-u(y)}{|x-y|^s}\\right)\\frac{dy}{|x-y|^{n+s}}, \\] being $g$ the derivative of a Young function. We further derive qualitative properties of solutions such as a Liouville type theorem and symmetry results and present several possible extensions and some interesting open questions. These are the first results of this type proved in this setting.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-25T18:25:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "symmetry results",
      "maximum principles",
      "liouville theorem",
      "liouville type theorem",
      "non-local non-linear operators"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}