{
  "id": "1710.07760",
  "version": "v1",
  "published": "2017-10-21T06:14:34.000Z",
  "updated": "2017-10-21T06:14:34.000Z",
  "title": "Equivalence of viscosity and weak solutions for the normalized $p(x)$-Laplacian",
  "authors": [
    "Jarkko Siltakoski"
  ],
  "comment": "20 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We show that viscosity solutions to the normalized $p(x)$-Laplace equation coincide with distributional weak solutions to the strong $p(x)$-Laplace equation when $p$ is Lipschitz and $\\inf p>1$. This yields $C^{1,\\alpha}$ regularity for the viscosity solutions of the normalized $p(x)$-Laplace equation. As an additional application, we prove a Rad\\'o-type removability theorem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-21T06:14:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J60",
      "35D40",
      "35D30"
    ],
    "keywords": [
      "equivalence",
      "viscosity solutions",
      "laplace equation coincide",
      "rado-type removability theorem",
      "distributional weak solutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}