{
  "id": "1606.07751",
  "version": "v1",
  "published": "2016-06-24T16:34:26.000Z",
  "updated": "2016-06-24T16:34:26.000Z",
  "title": "Beltrami equations in the plane and Sobolev regularity",
  "authors": [
    "Martí Prats"
  ],
  "comment": "16 pages, 12 figures",
  "categories": [
    "math.AP",
    "math.CA"
  ],
  "abstract": "Some new results regarding the Sobolev regularity of the principal solution of the linear Beltrami equation $\\bar{\\partial} f = \\mu \\partial f + \\nu \\bar{\\partial f}$ for discontinuous Beltrami coefficients $\\mu$ and $\\nu$ are obtained, using Kato-Ponce commutators. A conjecture on the cases where the limitations of the method do not work is raised.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-06-24T16:34:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J46",
      "30C62",
      "46L36"
    ],
    "keywords": [
      "sobolev regularity",
      "linear beltrami equation",
      "discontinuous beltrami coefficients",
      "principal solution",
      "kato-ponce commutators"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}