{
  "id": "1705.03718",
  "version": "v1",
  "published": "2017-05-10T12:17:48.000Z",
  "updated": "2017-05-10T12:17:48.000Z",
  "title": "Schroedinger operators involving singular potentials and measure data",
  "authors": [
    "Augusto C. Ponce",
    "Nicolas Wilmet"
  ],
  "comment": "Accepted for publication in Journal of Differential Equations",
  "doi": "10.1016/j.jde.2017.04.039",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the existence of solutions of the Dirichlet problem for the Schroedinger operator with measure data $$ \\left\\{ {2} -\\Delta u + Vu &= \\mu and \\quad \\text{in \\(\\Omega\\)}, u &= 0 && \\quad \\text{on \\(\\partial\\Omega\\)}. \\right. $$ We characterize the finite measures $\\mu$ for which this problem has a solution for every nonnegative potential $V$ in the Lebesgue space $L^p(\\Omega)$ with $1 \\le p \\le N/2$. The full answer can be expressed in terms of the $W^{2,p}$ capacity for $p > 1$, and the $W^{1,2}$ (or Newtonian) capacity for $p = 1$. We then prove the existence of a solution of the problem above when $V$ belongs to the real Hardy space $H^1(\\Omega)$ and $\\mu$ is diffuse with respect to the $W^{2,1}$ capacity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-05-10T12:17:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J10",
      "35J15",
      "31B15",
      "31B35"
    ],
    "keywords": [
      "measure data",
      "schroedinger operator",
      "singular potentials",
      "real hardy space",
      "lebesgue space"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}