{
  "id": "math-ph/0411053",
  "version": "v1",
  "published": "2004-11-16T15:05:33.000Z",
  "updated": "2004-11-16T15:05:33.000Z",
  "title": "Accurate estimates for magnetic bottles in connection with superconductivity",
  "authors": [
    "S. Fournais",
    "B. Helffer"
  ],
  "comment": "51 pages",
  "categories": [
    "math-ph",
    "math.MP",
    "math.SP"
  ],
  "abstract": "Motivated by the theory of superconductivity and more precisely by the problem of the onset of superconductivity in dimension two, many papers devoted to the analysis in a semi-classical regime of the lowest eigenvalue of the Schr\\\"odinger operator with magnetic field have appeared recently. Here we would like to mention the works by Bernoff-Sternberg, Lu-Pan, Del Pino-Felmer-Sternberg and Helffer-Morame and also Bauman-Phillips-Tang for the case of a disc. In the present paper we settle one important part of this question completely by proving an asymptotic expansion to all orders for low-lying eigenvalues for generic domains. The word `generic' means in this context that the curvature of the boundary of the domain has a unique non-degenerate maximum.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-11-16T15:05:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "magnetic bottles",
      "accurate estimates",
      "superconductivity",
      "connection",
      "unique non-degenerate maximum"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 51,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math.ph..11053F"
    }
  }
}