{
  "id": "2110.04602",
  "version": "v2",
  "published": "2021-10-09T15:56:21.000Z",
  "updated": "2022-08-27T17:06:43.000Z",
  "title": "Ramification of multiple eigenvalues for the Dirichlet-Laplacian in perforated domains",
  "authors": [
    "Laura Abatangelo",
    "Corentin Léna",
    "Paolo Musolino"
  ],
  "comment": "42 pages, no figure. A few corrections (typos and notation) from the previous version. To appear in \"Journal of Functional Analysis\". arXiv admin note: text overlap with arXiv:1911.06686",
  "categories": [
    "math.AP",
    "math.SP"
  ],
  "abstract": "Taking advantage from the so-called \"Lemma on small eigenvalues\" by Colin de Verdi\\`ere, we study ramification for multiple eigenvalues of the Dirichlet Laplacian in bounded perforated domains. The asymptotic behavior of multiple eigenvalues turns out to depend on the asymptotic expansion of suitable associated eigenfunctions. We treat the case of planar domains in details, thanks to the asymptotic expansion of a generalization of the so-called u-capacity which we compute in dimension 2. In this case multiple eigenvalues are proved to split essentially by different rates of convergence of the perturbed eigenvalues or by different coefficients in front of their expansion if the rate of two eigenbranches turns out to be the same.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2022-08-27T17:06:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35P20",
      "31C15",
      "31B10",
      "35B25",
      "35C20"
    ],
    "keywords": [
      "perforated domains",
      "dirichlet-laplacian",
      "asymptotic expansion",
      "multiple eigenvalues turns",
      "case multiple eigenvalues"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 42,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}