{
  "id": "math/0504268",
  "version": "v3",
  "published": "2005-04-13T11:27:52.000Z",
  "updated": "2005-08-19T08:53:47.000Z",
  "title": "Differentiation, implicit functions, and applications to generalized well-posedness",
  "authors": [
    "Seppo I Hiltunen"
  ],
  "comment": "AmS-TeX, 36 pages; v2: added some details of proof; v3: '4 Remarks' in Section 2 supplemented and modified, few misprints corrected",
  "categories": [
    "math.FA"
  ],
  "abstract": "This article is centered around generalizing a previous implicit function theorem of the author to be applicable for maps f:E sqcap F to F which can be lifted to Keller C^k_pi maps f_i:E sqcap F_i to F_i with F_i Banach and F=projlim F_i . We prove theorems about existence and differentiability of functions g satisfying f(x,g(x))=b constant. In addition to these abstract theorems, we give several examples of applications to proving smooth dependence of the solution on initial/boundary values and the nonlinearity in nonlinear (partial) differential equations.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2005-08-19T08:53:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58C15",
      "47J07",
      "46T20",
      "46T25",
      "35B30"
    ],
    "keywords": [
      "generalized well-posedness",
      "applications",
      "differentiation",
      "implicit function theorem",
      "abstract theorems"
    ],
    "note": {
      "typesetting": "AMS-TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......4268H"
    }
  }
}