{
  "id": "1406.6331",
  "version": "v1",
  "published": "2014-06-24T18:29:01.000Z",
  "updated": "2014-06-24T18:29:01.000Z",
  "title": "Dirichlet problems on graphs with ends",
  "authors": [
    "Tony Perkins"
  ],
  "comment": "13 pages",
  "doi": "10.1016/j.jmaa.2014.06.064",
  "categories": [
    "math.AP"
  ],
  "abstract": "In classical potential theory, one can solve the Dirichlet problem on unbounded domains such as the upper half plane. These domains have two types of boundary points; the usual finite boundary points and another point at infinity. W. Woess has solved a discrete version of the Dirichlet problem on the ends of graphs analogous to having multiple points at infinity and no finite boundary. Whereas C. Kiselman has solved a similar version of the Dirichlet problem on graphs analogous to bounded domains. In this work, we combine the two ideas to solve a version of the Dirichlet problem on graphs with finitely many ends and boundary points of the Kiselman type.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-06-24T18:29:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "31C20",
      "05A99",
      "31C05"
    ],
    "keywords": [
      "dirichlet problem",
      "usual finite boundary points",
      "upper half plane",
      "classical potential theory",
      "discrete version"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1406.6331P"
    }
  }
}