{
  "id": "0907.1006",
  "version": "v3",
  "published": "2009-07-06T14:26:08.000Z",
  "updated": "2009-07-16T17:30:47.000Z",
  "title": "Boundary trace of positive solutions of semilinear elliptic equations in Lipschitz domains",
  "authors": [
    "Moshe Marcus",
    "Laurent Veron"
  ],
  "comment": "120 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the generalized boundary value problem for nonnegative solutions of $-\\Delta u+g(u)=0$ in a bounded Lipschitz domain $\\Gw$, when $g$ is continuous and nondecreasing. Using the harmonic measure of $\\Gw$, 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 $\\Gw$ is (locally) a cone with vertex $y$, we prove sharp results of removability and characterization of singular behavior. In the general case, assuming that $\\Gw$ 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. We obtain sharp results involving Besov spaces with negative index on k-dimensional edges and apply our results to the characterization of removable sets and good measures on the boundary of a polyhedron.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2009-07-16T17:30:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "31A15",
      "31C15",
      "32A55",
      "35J60"
    ],
    "keywords": [
      "semilinear elliptic equations",
      "lipschitz domain",
      "positive solutions",
      "sharp results",
      "outer regular borel measures"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 120,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0907.1006M"
    }
  }
}