{
  "id": "1705.08007",
  "version": "v1",
  "published": "2017-05-22T21:18:02.000Z",
  "updated": "2017-05-22T21:18:02.000Z",
  "title": "Elliptic operators with unbounded diffusion, drift and potential terms",
  "authors": [
    "S. E. Boutiah",
    "F. Gregorio",
    "A. Rhandi",
    "C. Tacelli"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We prove that the realization $A_p$ in $L^p(\\mathbb{R}^N),\\,1<p<\\infty$, of the elliptic operator $A=(1+|x|^{\\alpha})\\Delta+b|x|^{\\alpha-1}\\frac{x}{|x|}\\cdot \\nabla-c|x|^{\\beta}$ 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 $T(\\cdot)$ provided that $\\alpha >2,\\,\\beta >\\alpha -2$ and any constants $b\\in \\mathbb{R}$ and $c>0$. This generalizes the recent results in [A.Canale, A. Rhandi, C. Tacelli, Ann. Sc. Norm. Super. Pisa CI. Sci. (5), 2016] and in [G.Metafune, C.Spina, C.Tacelli, Adv. Diff. Equat., 2014]. Moreover we show that $T(\\cdot)$ is consistent, immediately compact and ultracontractive.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-05-22T21:18:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "elliptic operator",
      "potential terms",
      "unbounded diffusion",
      "strongly continuous analytic semigroup",
      "pisa ci"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}