{
  "id": "1911.03151",
  "version": "v1",
  "published": "2019-11-08T09:46:03.000Z",
  "updated": "2019-11-08T09:46:03.000Z",
  "title": "Schauder and Sobolev Estimates of Parabolic Equations",
  "authors": [
    "Guangying Lv",
    "Jinlong Wei"
  ],
  "comment": "6 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this note, we use the non-homogeneous Poisson stochastic process to show how knowing Schauder and Sobolev estimates for the one-dimensional heat equation allows one to derive their multidimensional analogs. The method is probability. We generalize the result of Krylov-Priola [7].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-11-08T09:46:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "sobolev estimates",
      "parabolic equations",
      "one-dimensional heat equation",
      "non-homogeneous poisson stochastic process",
      "multidimensional analogs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}