{
  "id": "math/9504226",
  "version": "v1",
  "published": "1995-04-01T00:00:00.000Z",
  "updated": "1995-04-01T00:00:00.000Z",
  "title": "A Formula for Finding a Potential from Nodal Lines",
  "authors": [
    "Joyce R. McLaughlin",
    "Ole H. Hald"
  ],
  "comment": "7 pages",
  "journal": "Bull. Amer. Math. Soc. (N.S.) 32 (1995) 241-247",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this announcement we consider an eigenvalue problem which arises in the study of rectangular membranes. The mathematical model is an elliptic equation, in potential form, with Dirichlet boundary conditions. We have shown that the potential is uniquely determined, up to an additive constant, by a subset of the nodal lines of the eigenfunctions. A formula is given which, when the additive constant is fixed, yields an approximation to the potential at a dense set of points. An estimate is presented for the error made by the formula.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1995-04-01T00:00:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nodal lines",
      "additive constant",
      "dirichlet boundary conditions",
      "eigenvalue problem",
      "potential form"
    ],
    "tags": [
      "journal article",
      "expository article"
    ],
    "publication": {
      "publisher": "AMS",
      "journal": "Bull. Amer. Math. Soc."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1995math......4226M"
    }
  }
}