{
  "id": "0811.2982",
  "version": "v1",
  "published": "2008-11-18T20:41:24.000Z",
  "updated": "2008-11-18T20:41:24.000Z",
  "title": "On confining potentials and essential self-adjointness for Schrödinger operators on bounded domains in R^n",
  "authors": [
    "Gh. Nenciu",
    "I. Nenciu"
  ],
  "categories": [
    "math-ph",
    "math.MP",
    "math.SP"
  ],
  "abstract": "Let $\\Omega$ be a bounded domain in $R^n$ with $C^2$-smooth boundary of co-dimension 1, and let $H=-\\Delta +V(x)$ be a Schr\\\"odinger operator on $\\Omega$ with potential V locally bounded. We seek the weakest conditions we can find on the rate of growth of the potential V close to the boundary which guarantee essential self-adjointness of H on $C_0^\\infty(\\Omega)$. As a special case of an abstract condition, we add optimal logarithmic type corrections to the known condition $V(x)\\geq \\frac{3}{4d(x)^2}$, where $d(x)=dist(x,\\partial\\Omega)$. The constant 1 in front of each logarithmic term in Theorem 2 is optimal. The proof is based on a refined Agmon exponential estimate combined with a well known multidimensional Hardy inequality.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-11-18T20:41:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "bounded domain",
      "schrödinger operators",
      "confining potentials",
      "add optimal logarithmic type corrections",
      "guarantee essential self-adjointness"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009AnHP...10..377N"
    }
  }
}