{
  "id": "2203.09272",
  "version": "v1",
  "published": "2022-03-17T11:56:09.000Z",
  "updated": "2022-03-17T11:56:09.000Z",
  "title": "An inverse problem for the minimal surface equation",
  "authors": [
    "Janne Nurminen"
  ],
  "comment": "24 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We use the method of higher order linearization to study an inverse boundary value problem for the minimal surface equation on a Riemannian manifold $(\\mathbb{R}^{n},g)$, where the metric $g$ is conformally Euclidean. In particular we show that with the knowledge of Dirichlet-to-Neumann map associated to the minimal surface equation, one can determine the Taylor series of the conformal factor $c(x)$ at $x_n=0$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-03-17T11:56:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R30",
      "35J25",
      "35J61"
    ],
    "keywords": [
      "minimal surface equation",
      "inverse problem",
      "inverse boundary value problem",
      "higher order linearization",
      "dirichlet-to-neumann map"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}