{
  "id": "2105.15016",
  "version": "v1",
  "published": "2021-05-31T14:54:39.000Z",
  "updated": "2021-05-31T14:54:39.000Z",
  "title": "Weak Harnack inequality for a mixed local and nonlocal parabolic equation",
  "authors": [
    "Prashanta Garain",
    "Juha Kinnunen"
  ],
  "comment": "27 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "This article proves a weak Harnack inequality with a tail term for sign changing supersolutions of a mixed local and nonlocal parabolic equation. Our argument is purely analytic. It is based on energy estimates and the Moser iteration technique. Instead of the parabolic John-Nirenberg lemma, we adopt a lemma of Bombieri to the mixed local and nonlocal parabolic case. To this end, we prove an appropriate reverse H\\\"older inequality and a logarithmic estimate for weak supersolutions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-05-31T14:54:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R11",
      "35K05",
      "35B65",
      "47G20",
      "35D30"
    ],
    "keywords": [
      "weak harnack inequality",
      "nonlocal parabolic equation",
      "mixed local",
      "nonlocal parabolic case",
      "parabolic john-nirenberg lemma"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}