{
  "id": "1603.00612",
  "version": "v1",
  "published": "2016-03-02T08:33:35.000Z",
  "updated": "2016-03-02T08:33:35.000Z",
  "title": "Gradient Estimates via Rearrangements for Solutions of Some Schrödinger Equations",
  "authors": [
    "Sibei Yang",
    "Der-Chen Chang",
    "Dachun Yang",
    "Zunwei Fu"
  ],
  "comment": "26 pages; submitted",
  "categories": [
    "math.AP",
    "math.CA"
  ],
  "abstract": "In this article, by applying the well known method for dealing with $p$-Laplace type elliptic boundary value problems, the authors establish a sharp estimate for the decreasing rearrangement of the gradient of solutions to the Dirichlet and the Neumann boundary value problems of a class of Schr\\\"odinger equations, under the weak regularity assumption on the boundary of domains. As applications, gradient estimates of these solutions in Lebesgue spaces and Lorentz spaces are obtained.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-03-02T08:33:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J10",
      "46E30",
      "35J25",
      "35D30",
      "35B45"
    ],
    "keywords": [
      "gradient estimates",
      "schrödinger equations",
      "rearrangement",
      "laplace type elliptic boundary value",
      "type elliptic boundary value problems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160300612Y"
    }
  }
}