{
  "id": "1907.00882",
  "version": "v1",
  "published": "2019-07-01T15:55:26.000Z",
  "updated": "2019-07-01T15:55:26.000Z",
  "title": "An overview on constrained critical points of Dirichlet integrals",
  "authors": [
    "Lorenzo Brasco",
    "Giovanni Franzina"
  ],
  "comment": "41 pages, 5 figures. This paper evolved from a set of notes for a talk delivered by the first author at the workshop \"Nonlinear Meeting in Turin 2019\"",
  "categories": [
    "math.AP",
    "math.SP"
  ],
  "abstract": "We consider a natural generalization of the eigenvalue problem for the Laplacian with homogeneous Dirichlet boundary conditions. This corresponds to look for the critical values of the Dirichlet integral, constrained to the unit $L^q$ sphere. We collect some results, present some counter-examples and compile a list of open problems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-01T15:55:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35P30",
      "49R05"
    ],
    "keywords": [
      "constrained critical points",
      "dirichlet integral",
      "homogeneous dirichlet boundary conditions",
      "eigenvalue problem",
      "open problems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 41,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}