{
  "id": "1405.5866",
  "version": "v1",
  "published": "2014-05-22T19:31:42.000Z",
  "updated": "2014-05-22T19:31:42.000Z",
  "title": "Stochastic variational inequalities and regularity for degenerate stochastic partial differential equations",
  "authors": [
    "Benjamin Gess",
    "Michael Röckner"
  ],
  "comment": "26 pages",
  "categories": [
    "math.PR",
    "math.AP"
  ],
  "abstract": "The regularity and characterization of solutions to degenerate, quasilinear SPDE is studied. Our results are two-fold: First, we prove regularity results for solutions to certain degenerate, quasilinear SPDE driven by Lipschitz continuous noise. In particular, this provides a characterization of solutions to such SPDE in terms of (generalized) strong solutions. Second, for the one-dimensional stochastic mean curvature flow with normal noise we adapt the notion of stochastic variational inequalities to provide a characterization of solutions previously obtained in a limiting sense only. This solves a problem left open in [Es-Sarhir, von Renesse; SIAM, 2012] and sharpens regularity properties obtained in [Es-Sarhir, von Renesse, Stannat; NoDEA, 2012].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-05-22T19:31:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H15",
      "35R60",
      "35K93"
    ],
    "keywords": [
      "degenerate stochastic partial differential equations",
      "stochastic variational inequalities",
      "stochastic mean curvature flow",
      "regularity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1405.5866G"
    }
  }
}