{
  "id": "1011.1288",
  "version": "v1",
  "published": "2010-11-04T22:38:36.000Z",
  "updated": "2010-11-04T22:38:36.000Z",
  "title": "An Inverse Function Theorem in Frechet Spaces",
  "authors": [
    "Ivar Ekeland"
  ],
  "comment": "to appear, Annales de l'Institut Henri Poincare, Analyse Non Lineaire",
  "categories": [
    "math.FA"
  ],
  "abstract": "I present an inverse function theorem for differentiable maps between Frechet spaces which contains the classical theorem of Nash and Moser as a particular case. In contrast to the latter, the proof does not rely on the Newton iteration procedure, but on Lebesgue's dominated convergence theorem and Ekeland's variational principle. As a consequence, the assumptions are substantially weakened: the map F to be inverted is not required to be C^2, or even C^1, or even Frechet-differentiable.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-11-04T22:38:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "inverse function theorem",
      "frechet spaces",
      "ekelands variational principle",
      "lebesgues dominated convergence theorem",
      "newton iteration procedure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}