{
  "id": "1507.08846",
  "version": "v1",
  "published": "2015-07-31T12:13:02.000Z",
  "updated": "2015-07-31T12:13:02.000Z",
  "title": "Existence of solutions for semilinear elliptic boundary value problems on arbitrary open sets",
  "authors": [
    "Reinhard Stahn"
  ],
  "comment": "13 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We show the existence of a weak solution of a semilinear elliptic Dirichlet problem on an arbitrary open set. We make no assumptions about the open set, very mild regularity assumptions on the semilinearity, plus a coerciveness assumption which depends on the optimal Poincare-Steklov constant. The proof is based on Schaefer's fixed point theorem applied to a sequence of truncated problems. We state a simple uniqueness result. We also generalize the results to Robin boundary conditions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-07-31T12:13:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35A16"
    ],
    "keywords": [
      "semilinear elliptic boundary value problems",
      "arbitrary open set",
      "fixed point theorem",
      "semilinear elliptic dirichlet problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150708846S"
    }
  }
}