{
  "id": "1901.02588",
  "version": "v1",
  "published": "2019-01-09T03:22:22.000Z",
  "updated": "2019-01-09T03:22:22.000Z",
  "title": "Maximum principle for state constrained optimal control problems governed by multisolution p-Laplacian elliptic equations in the absence of convexity",
  "authors": [
    "Hongwei Lou",
    "Shu Luan"
  ],
  "comment": "25 pages",
  "categories": [
    "math.OC"
  ],
  "abstract": "A state constrained optimal control problem governed by a class of multisolution p-Laplacian elliptic equations is studied in this paper. Both the control domain and cost functional considered may be non-convex. Combining the multiplicity and degeneracy of the state equation with the non-convex assumptions is the main difficulty we will overcome. By transforming the initial problem to a well-posed and non degenerate problem with a point-point mixed constraint and then using Ekeland's variational principle, the Pontryagin's maximum principle for the initial problem is obtained by passing to the limits twice.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-01-09T03:22:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "49K20",
      "35J70"
    ],
    "keywords": [
      "state constrained optimal control problem",
      "multisolution p-laplacian elliptic equations",
      "maximum principle"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}