{
  "id": "0908.2327",
  "version": "v1",
  "published": "2009-08-17T11:22:05.000Z",
  "updated": "2009-08-17T11:22:05.000Z",
  "title": "Asymptotics of Dirichlet eigenvalues and eigenfunctions of the Laplacian on thin domains in R^d",
  "authors": [
    "Denis Borisov",
    "Pedro Freitas"
  ],
  "categories": [
    "math.AP",
    "math.SP"
  ],
  "abstract": "We consider the Laplace operator with Dirichlet boundary conditions on a domain in R^d and study the effect that performing a scaling in one direction has on the eigenvalues and corresponding eigenfunctions as a function of the scaling parameter around zero. This generalizes our previous results in two dimensions and, as in that case, allows us to obtain an approximation for Dirichlet eigenvalues for a large class of domains, under very mild assumptions. As an application, we derive a three--term asymptotic expansion for the first eigenvalue of d-dimensional ellipsoids.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-08-17T11:22:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dirichlet eigenvalues",
      "thin domains",
      "eigenfunctions",
      "dirichlet boundary conditions",
      "three-term asymptotic expansion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0908.2327B"
    }
  }
}