{
  "id": "2308.06090",
  "version": "v1",
  "published": "2023-08-11T12:04:18.000Z",
  "updated": "2023-08-11T12:04:18.000Z",
  "title": "Transformation of a variational problem in the Euclidean space to that of a tuple of functions on several regions",
  "authors": [
    "Sohei Ashida"
  ],
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We obtain a method to transform an minimization problem of the quadratic form corresponding to the Schr\\\"odinger operator in the Euclidean space to a variational problem of a tuple of functions defined on several regions. The method is based on a characterization of elements of the orthogonal complement of $H^1_0(\\Omega)$ in $H^1(\\Omega)$ as weak solutions to an elliptic partial differential equation on a region $\\Omega$ with a bounded boundary.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-08-11T12:04:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J10",
      "35J20",
      "47A75"
    ],
    "keywords": [
      "euclidean space",
      "variational problem",
      "transformation",
      "elliptic partial differential equation",
      "minimization problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}