{
  "id": "1007.2482",
  "version": "v1",
  "published": "2010-07-15T06:02:21.000Z",
  "updated": "2010-07-15T06:02:21.000Z",
  "title": "Boundary value problems with measures for elliptic equations with singular potentials",
  "authors": [
    "Laurent Veron",
    "Cecilia Yarur"
  ],
  "comment": "Contient un Appendice d'A. Ancona intitul\\'e A necessary condition for the fine regularity of a boundary point with respect to a Schr\\\"odinger equation",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the boundary value problem with Radon measures for nonnegative solutions of $L_Vu:=-\\Delta u+Vu=0$ in a bounded smooth domain $\\Gw$, when $V$ is a locally bounded nonnegative function. Introducing some specific capacity, we give sufficient conditions on a Radon measure $\\gm$ on $\\prt\\Gw$ so that the problem can be solved. We study the reduced measure associated to this equation as well as the boundary trace of positive solutions. In the appendix A. Ancona solves a question raised by M. Marcus and L. V\\'eron concerning the vanishing set of the Poisson kernel of $L_V$ for an important class of potentials $V$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-07-15T06:02:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "boundary value problem",
      "elliptic equations",
      "singular potentials",
      "radon measure",
      "poisson kernel"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1007.2482V"
    }
  }
}