{
  "id": "1804.04465",
  "version": "v1",
  "published": "2018-04-12T12:27:15.000Z",
  "updated": "2018-04-12T12:27:15.000Z",
  "title": "Explicit $\\infty$-harmonic functions in high dimensions",
  "authors": [
    "Birzhan Ayanbayev"
  ],
  "comment": "14 pages, 28 figures",
  "categories": [
    "math.AP"
  ],
  "abstract": "The aim of this work is to derive new explicit solutions to the $\\infty$-Laplace equation, the fundamental PDE arising in Calculus of Variations in the space $L^\\infty$. These solutions obey certain symmetry conditions and are derived in arbitrary dimensions, containing as particular sub-cases the already known classes two-dimensional infinity-harmonic functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-04-12T12:27:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "high dimensions",
      "classes two-dimensional infinity-harmonic functions",
      "laplace equation",
      "fundamental pde",
      "arbitrary dimensions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}