{
  "id": "2011.10964",
  "version": "v1",
  "published": "2020-11-22T08:15:04.000Z",
  "updated": "2020-11-22T08:15:04.000Z",
  "title": "Higher regularity for parabolic equations based on maximal L_p-L_q spaces",
  "authors": [
    "Naoto Kajiwara"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we prove higher regularity for 2m-th order parabolic equations with general boundary conditions. This is a kind of maximal L_p-L_q regularity with differentiability, i.e. the main theorem is isomorphism between the solution space and the data space using Besov and Triebel--Lizorkin spaces. The key is compatibility conditions for the initial data. We are able to get a unique smooth solution if the data satisfying compatibility conditions are smooth.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-22T08:15:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "higher regularity",
      "2m-th order parabolic equations",
      "general boundary conditions",
      "unique smooth solution",
      "data satisfying compatibility conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}