{
  "id": "1409.6804",
  "version": "v1",
  "published": "2014-09-24T02:55:14.000Z",
  "updated": "2014-09-24T02:55:14.000Z",
  "title": "Everywhere differentiability of viscosity solutions to a class of Aronsson's equations",
  "authors": [
    "Juhana Siljander",
    "Changyou Wang",
    "Yuan Zhou"
  ],
  "comment": "24 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "For any open set $\\Omega\\subset\\mathbb R^n$ and $n\\ge 2$, we establish everywhere differentiability of viscosity solutions to the Aronsson equation $$ <D_x(H(x, Du)), D_p H(x, Du)>=0 \\quad \\rm in\\ \\ \\Omega, $$ where $H$ is given by $$H(x,\\,p)=<A(x)p,p>=\\sum_{i,\\,j=1}^na^{ij}(x)p_i p_j,\\ x\\in\\Omega, \\ p\\in\\mathbb R^n, $$ and $A=(a^{ij}(x))\\in C^{1,1}(\\bar\\Omega,\\mathbb R^{n\\times n})$ is uniformly elliptic. This extends an earlier theorem by Evans and Smart \\cite{es11a} on infinity harmonic functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-09-24T02:55:14.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "viscosity solutions",
      "aronssons equations",
      "differentiability",
      "infinity harmonic functions",
      "open set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1409.6804S"
    }
  }
}