{
  "id": "1008.2599",
  "version": "v1",
  "published": "2010-08-16T08:49:59.000Z",
  "updated": "2010-08-16T08:49:59.000Z",
  "title": "Elimination of Hamilton-Jacobi equation in extreme variational problems",
  "authors": [
    "Igor Orlov"
  ],
  "comment": "10 pages",
  "categories": [
    "math.OC",
    "math.AP",
    "math.FA"
  ],
  "abstract": "It is shown that extreme problem for one-dimensional Euler-Lagrange variational functional in $C^1[a;b]$ under the strengthened Legendre condition can be solved without using Hamilton-Jacobi equation. In this case, exactly one of the two possible cases requires a restriction to a length of $[a;b]$, defined only by the form of integrand. The result is extended to the case of compact extremum in $H^1[a;b]$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-08-16T08:49:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "49J05",
      "49L99",
      "G.1.6",
      "G.1.8"
    ],
    "keywords": [
      "extreme variational problems",
      "hamilton-jacobi equation",
      "elimination",
      "one-dimensional euler-lagrange variational functional",
      "strengthened legendre condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1008.2599O"
    }
  }
}