{
  "id": "1309.7778",
  "version": "v3",
  "published": "2013-09-30T09:52:53.000Z",
  "updated": "2014-07-02T08:11:56.000Z",
  "title": "Boundary trace of positive solutions of supercritical semilinear elliptic equations in dihedral domains",
  "authors": [
    "Moshe Marcus",
    "Laurent Veron"
  ],
  "comment": "To appear Ann. Sc.Norm. Sup. Pisa Cl. Sci. arXiv admin note: substantial text overlap with arXiv:0907.1006",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the generalized boundary value problem for (E)\\; $-\\Delta u+|u|^{q-1}u=0$ in a dihedral domain $\\Gw$, when $q>1$ is supercritical. The value of the critical exponent can take only a finite number of values depending on the geometry of $\\Gw$. When $\\gm$ is a bounded Borel measure in a k-wedge, we give necessary and sufficient conditions in order it be the boundary value of a solution of (E). We also give conditions which ensure that a boundary compact subset is removable. These conditions are expressed in terms of Bessel capacities $B_{s,q'}$ in $\\BBR^{N-k}$ where $s$ depends on the characteristics of the wedge. This allows us to describe the boundary trace of a positive solution of (E)",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-07-02T08:11:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "supercritical semilinear elliptic equations",
      "boundary trace",
      "dihedral domain",
      "positive solution",
      "boundary compact subset"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1309.7778M"
    }
  }
}