{
  "id": "1302.2204",
  "version": "v1",
  "published": "2013-02-09T07:52:55.000Z",
  "updated": "2013-02-09T07:52:55.000Z",
  "title": "Traces of Sobolev functions on regular surfaces in infinite dimensions",
  "authors": [
    "Pietro Celada",
    "Alessandra Lunardi"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In a Banach space $X$ endowed with a nondegenerate Gaussian measure, we consider Sobolev spaces of real functions defined in a sublevel set $O= \\{x\\in X:\\;G(x) <0\\}$ of a Sobolev nondegenerate function $G:X\\mapsto \\R$. We define the traces at $G^{-1}(0)$ of the elements of $W^{1,p}(O, \\mu)$ for $p>1$, as elements of $L^1(G^{-1}(0), \\rho)$ where $\\rho$ is the surface measure of Feyel and de La Pradelle. The range of the trace operator is contained in $L^q(G^{-1}(0), \\rho)$ for $1\\leq q<p$ and even in $L^p(G^{-1}(0), \\rho)$ under further assumptions. If $O$ is a suitable halfspace, the range is characterized as a sort of fractional Sobolev space at the boundary. An important consequence of the general theory is an integration by parts formula for Sobolev functions, which involves their traces at $G^{-1}(0)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-02-09T07:52:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E35",
      "28C20",
      "26E15"
    ],
    "keywords": [
      "sobolev functions",
      "regular surfaces",
      "infinite dimensions",
      "fractional sobolev space",
      "sobolev nondegenerate function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1302.2204C"
    }
  }
}