{
  "id": "1703.08649",
  "version": "v1",
  "published": "2017-03-25T04:55:23.000Z",
  "updated": "2017-03-25T04:55:23.000Z",
  "title": "Second-Order Necessary Conditions for Optimal Control of Semilinear Elliptic Equations with Leading Term Containing Controls",
  "authors": [
    "Hongwei Lou",
    "Jiongmin Yong"
  ],
  "comment": "28 pages",
  "categories": [
    "math.OC"
  ],
  "abstract": "An optimal control problem for a semilinear elliptic equation of divergence form is considered. Both the leading term and the semilinear term of the state equation contain the control. The well-known Pontryagin type maximum principle for the optimal controls is the first-order necessary condition. When such a first-order necessary condition is singular in some sense, certain type of the second-order necessary condition will come in naturally. The aim of this paper is to explore such kind of conditions for our optimal control problem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-25T04:55:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "49K20",
      "35J61",
      "35Q93"
    ],
    "keywords": [
      "second-order necessary condition",
      "semilinear elliptic equation",
      "leading term containing controls",
      "pontryagin type maximum principle",
      "first-order necessary condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}