{
  "id": "2011.13771",
  "version": "v1",
  "published": "2020-11-27T15:06:45.000Z",
  "updated": "2020-11-27T15:06:45.000Z",
  "title": "A non-local approach to the generalized Stokes operator with bounded measurable coefficients",
  "authors": [
    "Patrick Tolksdorf"
  ],
  "categories": [
    "math.AP",
    "math.FA"
  ],
  "abstract": "We establish functional analytic properties of the Stokes operator with bounded measurable coefficients on $L^p_{\\sigma} (\\mathbb{R}^d)$, $d \\geq 2$, for $\\lvert 1 / p - 1 / 2 \\rvert < 1 / d$. These include optimal resolvent bounds and the property of maximal $L^q$-regularity. We further give regularity estimates on the gradient of the solution to the Stokes resolvent problem with bounded measurable coefficients. As a key to these results we establish the validity of a non-local Caccioppoli inequality to solutions of the Stokes resolvent problem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-27T15:06:45.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "bounded measurable coefficients",
      "generalized stokes operator",
      "non-local approach",
      "stokes resolvent problem",
      "non-local caccioppoli inequality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}