{
  "id": "1008.4222",
  "version": "v2",
  "published": "2010-08-25T07:32:31.000Z",
  "updated": "2011-10-26T12:59:27.000Z",
  "title": "Boundary Trace of Positive Solutions of Semilinear Elliptic Equations in Lipschitz Domains: The Subcritical Case",
  "authors": [
    "Moshe Marcus",
    "Laurent Veron"
  ],
  "comment": "To appear in Annali Scuola Normale Superiore Pisa. arXiv admin note: substantial text overlap with arXiv:0907.1006",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the generalized boundary value problem for nonnegative solutions of of $-\\Delta u+g(u)=0$ in a bounded Lipschitz domain $\\Omega$, when $g$ is continuous and nondecreasing. Using the harmonic measure of $\\Omega$, we define a trace in the class of outer regular Borel measures. We amphasize the case where $g(u)=|u|^{q-1}u$, $q>1$. When $\\Omega$ is (locally) a cone with vertex $y$, we prove sharp results of removability and characterization of singular behavior. In the general case, assuming that $\\Omega$ possesses a tangent cone at every boundary point and $q$ is subcritical, we prove an existence and uniqueness result for positive solutions with arbitrary boundary trace.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-10-26T12:59:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "semilinear elliptic equations",
      "lipschitz domain",
      "positive solutions",
      "subcritical case",
      "outer regular borel measures"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1008.4222M"
    }
  }
}