{
  "id": "1412.4386",
  "version": "v2",
  "published": "2014-12-14T17:53:03.000Z",
  "updated": "2015-01-08T15:39:41.000Z",
  "title": "Weak subdifferentials, $r_L$-density and maximal monotonicity",
  "authors": [
    "Stephen Simons",
    "Xianfu Wang"
  ],
  "comment": "13 pages",
  "doi": "10.1007/s11228-015-0326-7",
  "categories": [
    "math.FA"
  ],
  "abstract": "In this paper, we first investigate an abstract subdifferential for which (using Ekeland's variational principle) we can prove an analog of the Br{\\o}ndsted-Rockafellar property. We introduce the \"$r_L$-density\" of a subset of the product of a Banach space with its dual. A closed $r_L$-dense monotone set is maximally monotone, but we will also consider the case of nonmonotone closed $r_L$-dense sets. As a special case of our results, we can prove Rockafellar's result that the subdifferential of a proper convex lower semicontinuous function is maximally monotone.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-12-14T17:53:03.000Z",
      "comment": "11 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-01-08T15:39:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "49J52",
      "47H04",
      "47H05",
      "65K10"
    ],
    "keywords": [
      "weak subdifferentials",
      "maximal monotonicity",
      "proper convex lower semicontinuous function",
      "ekelands variational principle",
      "maximally monotone"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Springer"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1412.4386S"
    }
  }
}