{
  "id": "1705.10232",
  "version": "v1",
  "published": "2017-05-29T15:06:26.000Z",
  "updated": "2017-05-29T15:06:26.000Z",
  "title": "$L^p$-estimates and regularity for SPDEs with monotone semilinearity",
  "authors": [
    "Neelima",
    "David Šiška"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "Semilinear stochastic partial differential equations on bounded domains $\\mathscr{D}$ are considered. The semilinear term may have arbitrary polynomial growth as long as it is continuous and monotone except perhaps near the origin. A typical example is the stochastic Ginzburg-Landau equation. The main result of this article are $L^p$-estimates for such equations. The $L^p$-estimates are subsequently employed in obtaining higher regularity. It is shown that the solution is continuous in time with values in the Sobolev space $H^2(\\mathscr{D}')$ and $L^2$-integrable with values in $H^3(\\mathscr{D}')$, for any $\\mathscr{D}'$ that is open and compactly contained in $\\mathscr{D}$. Analogous results are also obtained in weighted Sobolev spaces on the whole $\\mathscr{D}$ using results of Krylov 1994.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-05-29T15:06:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H15",
      "35R60"
    ],
    "keywords": [
      "monotone semilinearity",
      "regularity",
      "semilinear stochastic partial differential equations",
      "sobolev space",
      "arbitrary polynomial growth"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}