{
  "id": "1010.1712",
  "version": "v3",
  "published": "2010-10-08T15:01:34.000Z",
  "updated": "2015-10-27T13:55:59.000Z",
  "title": "Regularity for eigenfunctions of Schrödinger operators",
  "authors": [
    "Bernd Ammann",
    "Catarina Carvalho",
    "Victor Nistor"
  ],
  "comment": "to appear in Lett. Math. Phys",
  "journal": "Lett. Math. Phys. 101, 49-84 (2012)",
  "doi": "10.1007/s11005-012-0551-z",
  "categories": [
    "math-ph",
    "math.AP",
    "math.FA",
    "math.MP",
    "math.NA"
  ],
  "abstract": "We prove a regularity result in weighted Sobolev spaces (or Babuska--Kondratiev spaces) for the eigenfunctions of a Schr\\\"odinger operator. More precisely, let K_{a}^{m}(\\mathbb{R}^{3N}) be the weighted Sobolev space obtained by blowing up the set of singular points of the Coulomb type potential V(x) = \\sum_{1 \\le j \\le N} \\frac{b_j}{|x_j|} + \\sum_{1 \\le i < j \\le N} \\frac{c_{ij}}{|x_i-x_j|}, x in \\mathbb{R}^{3N}, b_j, c_{ij} in \\mathbb{R}. If u in L^2(\\mathbb{R}^{3N}) satisfies (-\\Delta + V) u = \\lambda u in distribution sense, then u belongs to K_{a}^{m} for all m \\in \\mathbb{Z}_+ and all a \\le 0. Our result extends to the case when b_j and c_{ij} are suitable bounded functions on the blown-up space. In the single-electron, multi-nuclei case, we obtain the same result for all a<3/2.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-02-17T16:20:46.000Z",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2015-10-27T13:55:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J10",
      "47F05",
      "58Z05",
      "65Z05"
    ],
    "keywords": [
      "schrödinger operators",
      "eigenfunctions",
      "weighted sobolev space",
      "coulomb type potential",
      "babuska-kondratiev spaces"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Springer",
      "journal": "Letters in Mathematical Physics",
      "year": 2012,
      "month": "Jul",
      "volume": 101,
      "number": 1,
      "pages": 49
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012LMaPh.101...49A"
    }
  }
}