{
  "id": "1705.05364",
  "version": "v1",
  "published": "2017-05-15T17:57:51.000Z",
  "updated": "2017-05-15T17:57:51.000Z",
  "title": "Boundary regularity of stochastic PDEs",
  "authors": [
    "Máté Gerencsér"
  ],
  "comment": "27 pages",
  "categories": [
    "math.PR",
    "math.AP"
  ],
  "abstract": "The boundary behaviour of solutions of stochastic PDEs with Dirichlet boundary conditions can be surprisingly - and in a sense, arbitrarily - bad: as shown by Krylov, for any $\\alpha>0$ one can find a simple $1$-dimensional constant coefficient linear equation whose solution at the boundary is not $\\alpha$-H\\\"older continuous. We obtain a positive counterpart of this: under some mild regularity assumptions on the coefficients, solutions of semilinear SPDEs on $C^1$ domains are proved to be $\\alpha$-H\\\"older continuous up to the boundary with some $\\alpha>0$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-05-15T17:57:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H15",
      "35R60"
    ],
    "keywords": [
      "stochastic pdes",
      "boundary regularity",
      "dimensional constant coefficient linear equation",
      "dirichlet boundary conditions",
      "mild regularity assumptions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}