{
  "id": "1001.0378",
  "version": "v1",
  "published": "2010-01-03T15:12:02.000Z",
  "updated": "2010-01-03T15:12:02.000Z",
  "title": "$L^{\\infty}$ estimates and integrability by compensation in Besov-Morrey spaces and applications",
  "authors": [
    "Laura Gioia Andrea Keller"
  ],
  "comment": "37 pages",
  "doi": "10.1515/ACV.2011.015",
  "categories": [
    "math.AP"
  ],
  "abstract": "$L^{\\infty}$ estimates in the integrability by compensation result of H. Wente fail in dimension larger than two when Sobolev spaces are replaced by the ad-hoc Morrey spaces. However, in this paper we prove that $L^{\\infty}$ estimates hold in arbitrary dimension when Morrey spaces are replaced by their Littlewood Paley counterparts: Besov-Morrey spaces. As an application we prove the existence of conservation laws to solution of elliptic systems of the form $-\\Delta u= \\Omega \\cdot \\nabla u$ where $\\Omega$ is antisymmetric and both $\\nabla u$ and $\\Omega$ belong to these Besov-Morrey spaces for which the system is critical.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-01-03T15:12:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J60",
      "58E20"
    ],
    "keywords": [
      "besov-morrey spaces",
      "application",
      "integrability",
      "littlewood paley counterparts",
      "ad-hoc morrey spaces"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 37,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}