{
  "id": "1701.08326",
  "version": "v1",
  "published": "2017-01-28T22:10:09.000Z",
  "updated": "2017-01-28T22:10:09.000Z",
  "title": "On the well-posedness of SPDEs with singular drift in divergence form",
  "authors": [
    "Carlo Marinelli",
    "Luca Scarpa"
  ],
  "comment": "11 pages",
  "categories": [
    "math.AP",
    "math.PR"
  ],
  "abstract": "We prove existence and uniqueness of strong solutions for a class of second-order stochastic PDEs with multiplicative Wiener noise and drift of the form $\\operatorname{div} \\gamma(\\nabla \\cdot)$, where $\\gamma$ is a maximal monotone graph in $\\mathbb{R}^n \\times \\mathbb{R}^n$ obtained as the subdifferential of a convex function satisfying very mild assumptions on its behavior at infinity. The well-posedness result complements the corresponding one in our recent work arXiv:1612.08260 where, under the additional assumption that $\\gamma$ is single-valued, a solution with better integrability and regularity properties is constructed. The proof given here, however, is self-contained.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-01-28T22:10:09.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "divergence form",
      "singular drift",
      "second-order stochastic pdes",
      "well-posedness result complements",
      "maximal monotone graph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}