{
  "id": "1406.0316",
  "version": "v1",
  "published": "2014-06-02T10:27:53.000Z",
  "updated": "2014-06-02T10:27:53.000Z",
  "title": "Schrödinger type operators with unbounded diffusion and potential terms",
  "authors": [
    "Anna Canale",
    "Abdelaziz Rhandi",
    "Cristian Tacelli"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We prove that the realization $A_p$ in $L^p(\\mathbb{R}^N),\\,1<p<\\infty$, of the Schr\\\"odinger type operator $A=(1+|x|^{\\alpha})\\Delta-|x|^{\\beta}$ with domain $D(A_p)=\\{u\\in W^{2,p}(\\mathbb{R}^N): Au\\in L^p(\\mathbb{R}^N)\\}$ generates a strongly continuous analytic semigroup provided that $N>2,\\,\\alpha >2$ and $\\beta >\\alpha -2$. Moreover this semigroup is consistent, irreducible, immediately compact and ultracontractive.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-06-02T10:27:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47D07",
      "35J10"
    ],
    "keywords": [
      "schrödinger type operators",
      "potential terms",
      "unbounded diffusion",
      "strongly continuous analytic semigroup",
      "realization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1406.0316C"
    }
  }
}