{
  "id": "1705.10158",
  "version": "v1",
  "published": "2017-05-29T13:04:10.000Z",
  "updated": "2017-05-29T13:04:10.000Z",
  "title": "Dirichlet-to-Neumann and elliptic operators on C 1+$κ$ -domains: Poisson and Gaussian bounds",
  "authors": [
    "A. F. M. Ter Elst",
    "El Maati Ouhabaz"
  ],
  "categories": [
    "math.AP",
    "math.FA"
  ],
  "abstract": "We prove Poisson upper bounds for the heat kernel of the Dirichlet-to-Neumann operator with variable H{\\\"o}lder coefficients when the underlying domain is bounded and has a C 1+$\\kappa$-boundary for some $\\kappa$ > 0. We also prove a number of other results such as gradient estimates for heat kernels and Green functions G of elliptic operators with possibly complex-valued coefficients. We establish H{\\\"o}lder continuity of $\\nabla$ x $\\nabla$ y G up to the boundary. These results are used to prove L p-estimates for commutators of Dirichlet-to-Neumann operators on the boundary of C 1+$\\kappa$-domains. Such estimates are the keystone in our approach for the Poisson bounds.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-05-29T13:04:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "elliptic operators",
      "gaussian bounds",
      "heat kernel",
      "dirichlet-to-neumann operator",
      "poisson upper bounds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}