{
  "id": "1406.7798",
  "version": "v1",
  "published": "2014-06-30T16:22:33.000Z",
  "updated": "2014-06-30T16:22:33.000Z",
  "title": "Quantitative estimates of strong unique continuation for anisotropic wave equations",
  "authors": [
    "Sergio Vessella"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "The main results of the present paper consist in some quantitative estimates for solutions to the wave equation $\\partial^2_{t}u-\\mbox{div}\\left(A(x)\\nabla_x u\\right)=0$. Such estimates imply the following strong unique continuation properties: (a) if $u$ is a solution to the the wave equation and $u$ is flat on a segment $\\{x_0\\}\\times J$ on the $t$ axis, then $u$ vanishes in a neighborhood of $\\{x_0\\}\\times J$. (b) Let u be a solution of the above wave equation in $\\Omega\\times J$ that vanishes on a a portion $Z\\times J$ where $Z$ is a portion of $\\partial\\Omega$ and $u$ is flat on a segment $\\{x_0\\}\\times J$, $x_0\\in Z$, then $u$ vanishes in a neighborhood of $\\{x_0\\}\\times J$. The property (a) has been proved by G. Lebeau, Comm. Part. Diff. Equat. 24 (1999), 777-783.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-06-30T16:22:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R25",
      "35B60",
      "35R30"
    ],
    "keywords": [
      "anisotropic wave equations",
      "quantitative estimates",
      "strong unique continuation properties",
      "main results",
      "neighborhood"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1406.7798V"
    }
  }
}