{
  "id": "2105.12977",
  "version": "v1",
  "published": "2021-05-27T07:42:20.000Z",
  "updated": "2021-05-27T07:42:20.000Z",
  "title": "Observation estimate for the heat equations with Neumann boundary condition via logarithmic convexity",
  "authors": [
    "Rémi Buffe",
    "Kim Dang Phung"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We prove an inequality of H\\\"older type traducing the unique continuation property at one time for the heat equation with a potential and Neumann boundary condition. The main feature of the proof is to overcome the propagation of smallness by a global approach using a refined parabolic frequency function method. It relies with a Carleman commutator estimate to obtain the logarithmic convexity property of the frequency function.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-05-27T07:42:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "neumann boundary condition",
      "logarithmic convexity",
      "heat equation",
      "observation estimate",
      "refined parabolic frequency function method"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}