{
  "id": "math/0612354",
  "version": "v1",
  "published": "2006-12-13T13:25:05.000Z",
  "updated": "2006-12-13T13:25:05.000Z",
  "title": "Estimates for the Sobolev trace constant with critical exponent and applications",
  "authors": [
    "J. Fernandez Bonder",
    "N. Saintier"
  ],
  "comment": "22 pages, submitted",
  "journal": "Ann. Mat. Pura Appl, 187 (2008), no. 4, 683--704.",
  "doi": "10.1007/s10231-007-0062-1",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we find estimates for the optimal constant in the critical Sobolev trace inequality $S\\|u\\|^p_{L^{p_*}(\\partial\\Omega) \\hookrightarrow \\|u\\|^p_{W^{1,p}(\\Omega)}$ that are independent of $\\Omega$. This estimates generalized those of [3] for general $p$. Here $p_* := p(N-1)/(N-p)$ is the critical exponent for the immersion and $N$ is the space dimension. Then we apply our results first to prove existence of positive solutions to a nonlinear elliptic problem with a nonlinear boundary condition with critical growth on the boundary, generalizing the results of [16]. Finally, we study an optimal design problem with critical exponent.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-12-13T13:25:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J20",
      "35P30"
    ],
    "keywords": [
      "sobolev trace constant",
      "critical exponent",
      "applications",
      "optimal design problem",
      "critical sobolev trace inequality"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....12354F"
    }
  }
}