{
  "id": "0709.2663",
  "version": "v1",
  "published": "2007-09-17T16:11:18.000Z",
  "updated": "2007-09-17T16:11:18.000Z",
  "title": "Regularity of the density for the stochastic heat equation",
  "authors": [
    "Carl Mueller",
    "David Nualart"
  ],
  "journal": "Electronic J. Prob., 13, paper 74, 2248-2258, (2008)",
  "categories": [
    "math.PR"
  ],
  "abstract": "We study the smoothness of the density of a semilinear heat equation with multiplicative spacetime white noise. Using Malliavin calculus, we reduce the problem to a question of negative moments of solutions of a linear heat equation with multiplicative white noise. Then we settle this question by proving that solutions to the linear equation have negative moments of all orders.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-09-17T16:11:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H07"
    ],
    "keywords": [
      "stochastic heat equation",
      "regularity",
      "multiplicative spacetime white noise",
      "negative moments",
      "semilinear heat equation"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0709.2663M"
    }
  }
}