{
  "id": "1104.4243",
  "version": "v1",
  "published": "2011-04-21T11:58:19.000Z",
  "updated": "2011-04-21T11:58:19.000Z",
  "title": "Strong Solutions for Stochastic Partial Differential Equations of Gradient Type",
  "authors": [
    "Benjamin Gess"
  ],
  "comment": "30 pages",
  "categories": [
    "math.PR",
    "math.AP",
    "math.FA"
  ],
  "abstract": "Unique existence of analytically strong solutions to stochastic partial differential equations (SPDE) with drift given by the subdifferential of a quasi-convex function and with general multiplicative noise is proven. The proof applies a genuinely new method of weighted Galerkin approximations based on the \"distance\" defined by the quasi-convex function. Spatial regularization of the initial condition analogous to the deterministic case is obtained. The results yield a unified framework which is applied to stochastic generalized porous media equations, stochastic generalized reaction diffusion equations and stochastic generalized degenerated p-Laplace equations. In particular, higher regularity for solutions of such SPDE is obtained.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-04-21T11:58:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35A15",
      "60H15",
      "46N10",
      "76S05",
      "35J92",
      "35K57"
    ],
    "keywords": [
      "stochastic partial differential equations",
      "strong solutions",
      "gradient type",
      "generalized reaction diffusion equations",
      "generalized porous media equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1104.4243G"
    }
  }
}