{
  "id": "1708.01899",
  "version": "v1",
  "published": "2017-08-06T15:08:33.000Z",
  "updated": "2017-08-06T15:08:33.000Z",
  "title": "Quantitative uniqueness of solutions to parabolic equations",
  "authors": [
    "Jiuyi Zhu"
  ],
  "comment": "23 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We investigate the quantitative uniqueness of solutions to parabolic equations with lower order terms on compact smooth manifolds. Quantitative uniqueness is a quantitative form of strong unique continuation property. We characterize quantitative uniqueness by the rate of vanishing. We can obtain the vanishing order of solutions by $C^{1, 1}$ norm of the potential functions, as well as the $L^\\infty$ norm of the coefficient functions. Some quantitative Carleman estimates and three cylinder inequalities are established.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-08-06T15:08:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantitative uniqueness",
      "parabolic equations",
      "strong unique continuation property",
      "compact smooth manifolds",
      "lower order terms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}