{
  "id": "2004.10682",
  "version": "v1",
  "published": "2020-04-22T16:35:23.000Z",
  "updated": "2020-04-22T16:35:23.000Z",
  "title": "Sobolev functions without compactly supported approximations",
  "authors": [
    "Giona Veronelli"
  ],
  "comment": "10 pages. Comments are welcome",
  "categories": [
    "math.AP",
    "math.DG",
    "math.FA"
  ],
  "abstract": "A basilar property and a useful tool in the theory of Sobolev spaces is the density of smooth compactly supported functions in the space $W^{k,p}(\\R^n)$ (i.e. the functions with weak derivatives of orders $0$ to $k$ in $L^p$). On Riemannian manifolds, it is well known that the same property remains valid under suitable geometric assumptions. However, on a complete non-compact manifold it can fail to be true in general, as we prove in this paper.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-22T16:35:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E35",
      "53C20"
    ],
    "keywords": [
      "compactly supported approximations",
      "sobolev functions",
      "property remains valid",
      "complete non-compact manifold",
      "smooth compactly supported functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}