{
  "id": "2204.04414",
  "version": "v1",
  "published": "2022-04-09T07:48:32.000Z",
  "updated": "2022-04-09T07:48:32.000Z",
  "title": "Lions' representation theorem and applications",
  "authors": [
    "Wolfgang Arendt",
    "Isabelle Chalendar",
    "Robert Eymard"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "The Representation Theorem of Lions (RTL) is a version of the Lax--Milgram Theorem where completeness of one of the spaces is not complete. In this paper, RTL is deduced from an operator-theoretical version on normed space. The main point of the paper is a theory of derivations, based on RTL, for which well-posedness is proved. One application concerns non-autonomous evolution equations with a new initial-value and a periodic boundary condition for the time variable.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-04-09T07:48:32.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "representation theorem",
      "application concerns non-autonomous evolution equations",
      "periodic boundary condition",
      "main point",
      "lax-milgram theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}