{
  "id": "math/0112008",
  "version": "v1",
  "published": "2001-12-01T16:01:58.000Z",
  "updated": "2001-12-01T16:01:58.000Z",
  "title": "The coarea formula for Sobolev mappings",
  "authors": [
    "Jan Maly",
    "David Swanson",
    "William P. Ziemer"
  ],
  "comment": "Submitted for publication, 16 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "We extend Federer's coarea formula to mappings $f$ belonging to the Sobolev class $W^{1,p}(R^n;R^m)$, $1 \\le m < n$, $p>m$, and more generally, to mappings with gradient in the Lorentz space $L^{m,1}(R^n)$. This is accomplished by showing that the graph of $f$ in $R^{n+m}$ is a Hausdorff $n$-rectifiable set.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2001-12-01T16:01:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E35",
      "46E30"
    ],
    "keywords": [
      "sobolev mappings",
      "extend federers coarea formula",
      "lorentz space",
      "sobolev class",
      "rectifiable set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math.....12008M"
    }
  }
}