{
  "id": "1510.05704",
  "version": "v1",
  "published": "2015-10-19T22:14:07.000Z",
  "updated": "2015-10-19T22:14:07.000Z",
  "title": "A Free Boundary Problem for the Parabolic Poisson Kernel",
  "authors": [
    "Max Engelstein"
  ],
  "comment": "91 pages. Comments welcome",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study parabolic chord arc domains, introduced by Hofmann, Lewis and Nystr\\\"om, and prove a free boundary regularity result below the continuous threshold. More precisely, we show that a Reifenberg flat, parabolic chord arc domain whose Poisson kernel has logarithm in VMO must in fact be a vanishing chord arc domain (i.e. satisfies a vanishing Carleson measure condition). This generalizes, to the parabolic setting, a result of Kenig and Toro and answers in the affirmative a question left open in the aforementioned paper of Hofmann et al. A key step in this proof is a classification of \"flat\" blowups for the parabolic problem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-19T22:14:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R35"
    ],
    "keywords": [
      "free boundary problem",
      "parabolic poisson kernel",
      "study parabolic chord arc domains",
      "free boundary regularity result",
      "question left open"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 91,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151005704E"
    }
  }
}