{
  "id": "math-ph/0607071",
  "version": "v2",
  "published": "2006-07-31T07:19:18.000Z",
  "updated": "2007-02-15T02:37:04.000Z",
  "title": "Strong diamagnetism for general domains and applications",
  "authors": [
    "S. Fournais",
    "B. Helffer"
  ],
  "comment": "A few typos corrected. One argument given in more details. Version to be published in AIF",
  "categories": [
    "math-ph",
    "math.MP",
    "math.SP"
  ],
  "abstract": "We consider the Neumann Laplacian with constant magnetic field on a regular domain. Let $B$ be the strength of the magnetic field, and let $\\lambda_1(B)$ be the first eigenvalue of the magnetic Neumann Laplacian on the domain. It is proved that $B \\mapsto \\lambda_1(B)$ is monotone increasing for large $B$. Combined with the results of \\cite{FournaisHelffer3}, this implies that all the `third' critical fields for strongly Type II superconductors coincide.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-02-15T02:37:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "general domains",
      "strong diamagnetism",
      "applications",
      "constant magnetic field",
      "magnetic neumann laplacian"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.ph...7071F"
    }
  }
}