{
  "id": "1301.1221",
  "version": "v1",
  "published": "2013-01-07T15:06:27.000Z",
  "updated": "2013-01-07T15:06:27.000Z",
  "title": "The Obstacle Problem for Quasilinear Stochastic PDEs with non-homogeneous operator",
  "authors": [
    "Denis Laurent",
    "Matoussi Anis",
    "Zhang Jing"
  ],
  "comment": "19 pages. arXiv admin note: substantial text overlap with arXiv:1202.3296, arXiv:1210.3445, arXiv:1201.1092",
  "categories": [
    "math.PR"
  ],
  "abstract": "We prove the existence and uniqueness of solution of the obstacle problem for quasilinear Stochastic PDEs with non-homogeneous second order operator. Our method is based on analytical technics coming from the parabolic potential theory. The solution is expressed as a pair $(u,\\nu)$ where $u$ is a predictable continuous process which takes values in a proper Sobolev space and $\\nu$ is a random regular measure satisfying minimal Skohorod condition. Moreover, we establish a maximum principle for local solutions of such class of stochastic PDEs. The proofs are based on a version of It\\^o's formula and estimates for the positive part of a local solution which is non-positive on the lateral boundary.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-01-07T15:06:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H15",
      "35R60"
    ],
    "keywords": [
      "quasilinear stochastic pdes",
      "obstacle problem",
      "non-homogeneous operator",
      "local solution",
      "measure satisfying minimal skohorod condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}