{
  "id": "1712.00950",
  "version": "v1",
  "published": "2017-12-04T08:29:50.000Z",
  "updated": "2017-12-04T08:29:50.000Z",
  "title": "Interpolation inequality at one time point for parabolic equations with time-independent coefficients and applications",
  "authors": [
    "Huaiqiang Yu",
    "Can Zhang"
  ],
  "comment": "40 pages",
  "categories": [
    "math.OC"
  ],
  "abstract": "In this paper, we study the H\\\"older-type interpolation inequality and observability inequality from measurable sets in time for parabolic equations either with L^p unbounded potentials or with electric potentials. The parabolic equations under consideration evolve in bounded C^{1,1} domains of R^N (N\\geq3) with homogeneous Neumann boundary conditions. The approach for the interpolation inequality is based on a modified reduction method and some stability estimates for the corresponding elliptic operator.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-04T08:29:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B60",
      "35K10",
      "93C20"
    ],
    "keywords": [
      "parabolic equations",
      "interpolation inequality",
      "time point",
      "time-independent coefficients",
      "applications"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}