{
  "id": "1106.1501",
  "version": "v1",
  "published": "2011-06-08T05:07:35.000Z",
  "updated": "2011-06-08T05:07:35.000Z",
  "title": "Lipschitz stability in an inverse problem for the wave equation",
  "authors": [
    "Lucie Baudouin"
  ],
  "categories": [
    "math.AP",
    "math.OC"
  ],
  "abstract": "We are interested in the inverse problem of the determination of the potential $p(x), x\\in\\Omega\\subset\\mathbb{R}^n$ from the measurement of the normal derivative $\\partial_\\nu u$ on a suitable part $\\Gamma_0$ of the boundary of $\\Omega$, where $u$ is the solution of the wave equation $\\partial_{tt}u(x,t)-\\Delta u(x,t)+p(x)u(x,t)=0$ set in $\\Omega\\times(0,T)$ and given Dirichlet boundary data. More precisely, we will prove local uniqueness and stability for this inverse problem and the main tool will be a global Carleman estimate, result also interesting by itself.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-06-08T05:07:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "inverse problem",
      "wave equation",
      "lipschitz stability",
      "dirichlet boundary data",
      "global carleman estimate"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1106.1501B"
    }
  }
}