{
  "id": "1702.04572",
  "version": "v1",
  "published": "2017-02-15T12:18:27.000Z",
  "updated": "2017-02-15T12:18:27.000Z",
  "title": "Hopf potentials for Schroedinger operators",
  "authors": [
    "Luigi Orsina",
    "Augusto C. Ponce"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We establish the Hopf boundary point lemma for the Schr\\\"odinger operator $-\\Delta + V$ involving singular potentials $V \\in L^{1}_{\\mathrm{loc}}(\\Omega)$: we have that either the Hopf lemma holds for every nonnegative supersolution which vanishes on $\\partial\\Omega$ or it fails for every such a supersolution, almost everywhere with respect to the surface measure on $\\partial\\Omega$. The proof relies on the existence of nontrivial solutions of the nonhomogeneous Dirichlet problem with boundary datum in $L^{\\infty}(\\partial\\Omega)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-02-15T12:18:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B05",
      "35B50",
      "31B15",
      "31B35"
    ],
    "keywords": [
      "hopf potentials",
      "schroedinger operators",
      "hopf boundary point lemma",
      "hopf lemma holds",
      "singular potentials"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}