{
  "id": "1310.6421",
  "version": "v1",
  "published": "2013-10-23T22:40:56.000Z",
  "updated": "2013-10-23T22:40:56.000Z",
  "title": "Hölder-continuity for the nonlinear stochastic heat equation with rough initial conditions",
  "authors": [
    "Le Chen",
    "Robert C. Dalang"
  ],
  "comment": "33 pages, 0 figures",
  "categories": [
    "math.PR"
  ],
  "abstract": "We study space-time regularity of the solution of the nonlinear stochastic heat equation in one spatial dimension driven by space-time white noise, with a rough initial condition. This initial condition is a locally finite measure $\\mu$ with, possibly, exponentially growing tails. We show how this regularity depends, in a neighborhood of $t=0$, on the regularity of the initial condition. On compact sets in which $t>0$, the classical H\\\"older-continuity exponents $\\frac{1}{4}-$ in time and $\\frac{1}{2}-$ in space remain valid. However, on compact sets that include $t=0$, the H\\\"older continuity of the solution is $\\left(\\frac{\\alpha}{2}\\wedge \\frac{1}{4}\\right)-$ in time and $\\left(\\alpha\\wedge \\frac{1}{2}\\right)-$ in space, provided $\\mu$ is absolutely continuous with an $\\alpha$-H\\\"older continuous density.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-10-23T22:40:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H15",
      "60G60",
      "35R60"
    ],
    "keywords": [
      "nonlinear stochastic heat equation",
      "rough initial condition",
      "hölder-continuity",
      "compact sets",
      "space-time white noise"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.6421C"
    }
  }
}