{
  "id": "2102.11532",
  "version": "v1",
  "published": "2021-02-23T07:45:22.000Z",
  "updated": "2021-02-23T07:45:22.000Z",
  "title": "Optimality of increasing stability for an inverse boundary value problem",
  "authors": [
    "Pu-Zhao Kow",
    "Gunther Uhlmann",
    "Jenn-Nan Wang"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this work we study the optimality of increasing stability of the inverse boundary value problem (IBVP) for Schr\\\"{o}dinger equation. The rigorous justification of increasing stability for the IBVP for Schr\\\"{o}dinger equation were established by Isakov \\cite{Isa11} and by Isakov, Nagayasu, Uhlmann, Wang of the paper \\cite{INUW14}. In \\cite{Isa11}, \\cite{INUW14}, the authors showed that the stability of this IBVP increases as the frequency increases in the sense that the stability estimate changes from a logarithmic type to a H\\\"{o}lder type. In this work, we prove that the instability changes from an exponential type to a H\\\"older type when the frequency increases. This result verifies that results in \\cite{Isa11}, \\cite{INUW14} are optimal.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-23T07:45:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J15",
      "35R25",
      "35R30"
    ],
    "keywords": [
      "inverse boundary value problem",
      "increasing stability",
      "optimality",
      "frequency increases",
      "stability estimate changes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}