{
  "id": "1012.3183",
  "version": "v2",
  "published": "2010-12-14T22:03:40.000Z",
  "updated": "2011-04-18T20:46:58.000Z",
  "title": "Strichartz estimates for Dirichlet-wave equations in two dimensions with applications",
  "authors": [
    "Hart F. Smith",
    "Christopher D. Sogge",
    "Chengbo Wang"
  ],
  "comment": "Final version, to appear in the Transactions of the AMS. 20 pages, 2 figures",
  "journal": "Transactions of the American Mathematical Society, 364 (2012), 3329-3347",
  "doi": "10.1090/S0002-9947-2012-05607-8",
  "categories": [
    "math.AP"
  ],
  "abstract": "We establish the Strauss conjecture for nontrapping obstacles when the spatial dimension $n$ is two. As pointed out in \\cite{HMSSZ} this case is more subtle than $n=3$ or 4 due to the fact that the arguments of the first two authors \\cite{SmSo00}, Burq \\cite{B} and Metcalfe \\cite{M} showing that local Strichartz estimates for obstactles imply global ones require that the Sobolev index, $\\gamma$, equal 1/2 when $n=2$. We overcome this difficulty by interpolating between energy estimates ($\\gamma =0$) and ones for $\\gamma=\\frac12$ that are generalizations of Minkowski space estimates of Fang and the third author \\cite{FaWa2}, \\cite{FaWa}, the second author \\cite{So08} and Sterbenz \\cite{St05}.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-04-18T20:46:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35L71"
    ],
    "keywords": [
      "dirichlet-wave equations",
      "applications",
      "local strichartz estimates",
      "minkowski space estimates",
      "obstactles imply global"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AMS",
      "journal": "Trans. Amer. Math. Soc."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1012.3183S"
    }
  }
}