{
  "id": "2109.00934",
  "version": "v1",
  "published": "2021-09-02T13:21:21.000Z",
  "updated": "2021-09-02T13:21:21.000Z",
  "title": "Mean value formulas for classical solutions to uniformly parabolic equations in divergence form",
  "authors": [
    "Emanuele Malagoli",
    "Diego Pallara",
    "Sergio Polidoro"
  ],
  "comment": "22 pages, 2 figures",
  "categories": [
    "math.AP"
  ],
  "abstract": "We prove surface and volume mean value formulas for classical solutions to uniformly parabolic equations in divergence form. We emphasize that our results only rely on the classical theory, and our arguments follow the lines used in the original theory of harmonic functions. We provide two proofs relying on two different formulations of the divergence theorem, one stated for sets with almost C^1-boundary, the other stated for sets with finite perimeter.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-09-02T13:21:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K10",
      "35B65"
    ],
    "keywords": [
      "uniformly parabolic equations",
      "divergence form",
      "classical solutions",
      "volume mean value formulas",
      "original theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}