{
  "id": "1901.02507",
  "version": "v1",
  "published": "2019-01-08T20:39:38.000Z",
  "updated": "2019-01-08T20:39:38.000Z",
  "title": "Equivalence of viscosity and weak solutions for a $p$-parabolic equation",
  "authors": [
    "Jarkko Siltakoski"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the relationship of viscosity and weak solutions to the equation \\[ \\smash{\\partial_{t}u-\\Delta_{p}u=f(Du)} \\] where $p>1$ and $f\\in C(\\mathbb{R}^{N})$ satisfies suitable assumptions. Our main result is that bounded viscosity supersolutions coincide with bounded lower semicontinuous weak supersolutions. Moreover, we prove the lower semicontinuity of weak supersolutions when $p\\geq2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-01-08T20:39:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K92",
      "35J60",
      "35D40",
      "35D30",
      "35B51"
    ],
    "keywords": [
      "weak solutions",
      "parabolic equation",
      "equivalence",
      "bounded lower semicontinuous weak supersolutions",
      "bounded viscosity supersolutions coincide"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}