{
  "id": "1712.09808",
  "version": "v1",
  "published": "2017-12-28T10:28:00.000Z",
  "updated": "2017-12-28T10:28:00.000Z",
  "title": "Kato square root problem with unbounded leading coefficients",
  "authors": [
    "Luis Escauriaza",
    "Steve Hofmann"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We prove the Kato conjecture for elliptic operators, $L=-\\nabla\\cdot\\left((\\mathbf A+\\mathbf D)\\nabla\\ \\right)$, with $\\mathbf A$ a complex measurable bounded coercive matrix and $\\mathbf D$ a measurable real-valued skew-symmetric matrix in $\\mathbb{R}^n$ with entries in $BMO(\\mathbb{R}^n)$;\\, i.e., the domain of $\\sqrt{L}\\,$ is the Sobolev space $\\dot H^1(\\mathbb{R}^n)$ in any dimension, with the estimate $\\|\\sqrt{L}\\, f\\|_2\\lesssim \\| \\nabla f\\|_2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-28T10:28:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B45",
      "35J15",
      "35J25",
      "35J70",
      "42B20",
      "42B37",
      "47A07",
      "47B44",
      "47D06"
    ],
    "keywords": [
      "kato square root problem",
      "unbounded leading coefficients",
      "measurable real-valued skew-symmetric matrix",
      "complex measurable bounded coercive matrix",
      "kato conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}