{
  "id": "1811.05538",
  "version": "v1",
  "published": "2018-11-13T21:52:53.000Z",
  "updated": "2018-11-13T21:52:53.000Z",
  "title": "Extensions of convex functions with prescribed subdifferentials",
  "authors": [
    "Daniel Azagra",
    "Juan Ferrera",
    "Javier Gómez-Gil",
    "Carlos Mudarra"
  ],
  "comment": "9 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "Let $E$ be an arbitrary subset of a Banach space $X$, $f: E \\rightarrow \\mathbb{R}$ be a function, and $G:E \\rightrightarrows X^*$ be a set-valued mapping. We give necessary and sufficient conditions on $f, G$ for the existence of a continuous convex extension $F: X \\rightarrow \\mathbb{R} $ of $f$ such that the subdifferential $\\partial F$ of $F$ coincides with $G$ on $E.$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-13T21:52:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "convex functions",
      "prescribed subdifferentials",
      "arbitrary subset",
      "banach space",
      "sufficient conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}