{
  "id": "1803.09562",
  "version": "v1",
  "published": "2018-03-26T13:03:28.000Z",
  "updated": "2018-03-26T13:03:28.000Z",
  "title": "On maximum and comparison principles for parabolic problems with the $p$-Laplacian",
  "authors": [
    "Vladimir Bobkov",
    "Peter Takac"
  ],
  "comment": "16 pages",
  "doi": "10.1007/s13398-018-0536-6",
  "categories": [
    "math.AP"
  ],
  "abstract": "We investigate strong and weak versions of maximum and comparison principles for a class of quasilinear parabolic equations with the $p$-Laplacian $$ \\partial_t u - \\Delta_p u = \\lambda |u|^{p-2} u + f(x,t) $$ under zero boundary and nonnegative initial conditions on a bounded cylindrical domain $\\Omega \\times (0, T)$, $\\lambda \\in \\mathbb{R}$, and $f \\in L^\\infty(\\Omega \\times (0, T))$. Several related counterexamples are given.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-03-26T13:03:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B50",
      "35B51",
      "35B30",
      "35K92"
    ],
    "keywords": [
      "comparison principles",
      "parabolic problems",
      "quasilinear parabolic equations",
      "zero boundary",
      "weak versions"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Springer"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}