{
  "id": "2103.03226",
  "version": "v1",
  "published": "2021-03-04T18:52:22.000Z",
  "updated": "2021-03-04T18:52:22.000Z",
  "title": "On off-diagonal decay properties of the generalized Stokes semigroup with bounded measurable coefficients",
  "authors": [
    "Patrick Tolksdorf"
  ],
  "comment": "12 pages",
  "categories": [
    "math.AP",
    "math.FA"
  ],
  "abstract": "We investigate off-diagonal decay properties of the generalized Stokes semigroup with bounded measurable coefficients on $\\mathrm{L}^2_{\\sigma} (\\mathbb{R}^d)$. Such estimates are well-known for elliptic equations in the form of pointwise heat kernel bounds and for elliptic systems in the form of integrated off-diagonal estimates. On our way to unveil this off-diagonal behavior we prove resolvent estimates in Morrey spaces $\\mathrm{L}^{2 , \\nu} (\\mathbb{R}^d)$ with $0 \\leq \\nu < 2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-04T18:52:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "off-diagonal decay properties",
      "generalized stokes semigroup",
      "bounded measurable coefficients",
      "pointwise heat kernel bounds",
      "elliptic systems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}