{
  "id": "1505.07579",
  "version": "v1",
  "published": "2015-05-28T07:53:16.000Z",
  "updated": "2015-05-28T07:53:16.000Z",
  "title": "A comparison principle for the porous medium equation and its consequences",
  "authors": [
    "Benny Avelin",
    "Teemu Lukkari"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We prove a comparison principle for the porous medium equation in more general open sets in $\\mathbb{R}^{n+1}$ than space-time cylinders. We apply this result in two related contexts: we establish a connection between a potential theoretic notion of the obstacle problem and a notion based on a variational inequality. We also prove the basic properties of the PME capacity, in particular that there exists a capacitary extremal which gives the capacity for compact sets.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-05-28T07:53:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K55",
      "31C15",
      "35K86"
    ],
    "keywords": [
      "porous medium equation",
      "comparison principle",
      "consequences",
      "general open sets",
      "potential theoretic notion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150507579A"
    }
  }
}