{
  "id": "1801.05261",
  "version": "v1",
  "published": "2018-01-16T14:06:01.000Z",
  "updated": "2018-01-16T14:06:01.000Z",
  "title": "Operators with Wentzell boundary conditions and the Dirichlet-to-Neumann operator",
  "authors": [
    "Tim Binz",
    "Klaus-Jochen Engel"
  ],
  "comment": "14 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "In this paper we relate the generator property of an operator $A$ with (abstract) generalized Wentzell boundary conditions on a Banach space $X$ and its associated (abstract) Dirichlet-to-Neumann operator $N$ acting on a \"boundary\" space $\\partial X$. Our approach is based on similarity transformations and perturbation arguments and allows to split $A$ into an operator $A_{00}$ with Dirichlet-type boundary conditions on a space $X_0$ of states having \"zero trace\" and the operator $N$. If $A_{00}$ generates an analytic semigroup, we obtain under a weak Hille--Yosida type condition that $A$ generates an analytic semigroup on $X$ if and only if $N$ does so on $\\partial X$. Here we assume that the (abstract) \"trace\" operator $L:X\\to\\partial X$ is bounded what is typically satisfied if $X$ is a space of continuous functions. Concrete applications are made to various second order differential operators.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-16T14:06:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47D06",
      "34G10",
      "47E05",
      "47F05"
    ],
    "keywords": [
      "dirichlet-to-neumann operator",
      "weak hille-yosida type condition",
      "analytic semigroup",
      "second order differential operators",
      "generalized wentzell boundary conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}