{
  "id": "1611.08177",
  "version": "v1",
  "published": "2016-11-24T13:29:09.000Z",
  "updated": "2016-11-24T13:29:09.000Z",
  "title": "The Laplacian on the unit square in a self-similar manner",
  "authors": [
    "Hua Qiu",
    "Haoran Tian"
  ],
  "comment": "13pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "In this paper, we show how to construct the standard Laplacian on the unit square in a self-similar manner. We rewrite the familiar mean value property of planar harmonic functions in terms of averge values on small squares, from which we could know how the planar self-similar resistance form and the Laplacian look like. This approach combines the constructive limit-of-difference-quotients method of Kigami for p.c.f. self-similar sets and the method of averages introduced by Kusuoka and Zhou for the Sierpinski carpet.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-11-24T13:29:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "28A80"
    ],
    "keywords": [
      "self-similar manner",
      "unit square",
      "planar self-similar resistance form",
      "familiar mean value property",
      "planar harmonic functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}