{
  "id": "1609.01749",
  "version": "v1",
  "published": "2016-09-05T10:29:12.000Z",
  "updated": "2016-09-05T10:29:12.000Z",
  "title": "Short note on energy maximization property of the first eigenfunction of the Laplacian",
  "authors": [
    "Hayk Mikayelyan"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider the Dirichlet-energy maximization problem of the solution $u_f$ of (\\ref{main}), among all functions $f\\in L^2(D)$, such that $\\|f\\|_2= 1$. We show that the two maximizers are the first eigenfunctions of the Laplacian with Dirichlet boundary condition $f=\\pm u_1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-09-05T10:29:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35P15",
      "35P99"
    ],
    "keywords": [
      "energy maximization property",
      "first eigenfunction",
      "short note",
      "dirichlet-energy maximization problem",
      "dirichlet boundary condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}