{
  "id": "1211.3655",
  "version": "v1",
  "published": "2012-11-15T16:51:38.000Z",
  "updated": "2012-11-15T16:51:38.000Z",
  "title": "The mixed problem for the Lamé system in two dimensions",
  "authors": [
    "Katharine A. Ott",
    "Russell M. Brown"
  ],
  "journal": "J. Diff. Equations, 254 (2013), 4373-4400",
  "doi": "10.1016/j.jde.2013.03.007",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider the mixed problem for $L$ the Lam\\'e system of elasticity in a bounded Lipschitz domain $ \\Omega\\subset\\reals ^2$. We suppose that the boundary is written as the union of two disjoint sets, $\\partial\\Omega =D\\cup N$. We take traction data from the space $L^p(N)$ and Dirichlet data from a Sobolev space $ W^{1,p}(D)$ and look for a solution $u$ of $Lu =0$ with the given boundary conditions. We give a scale invariant condition on $D$ and find an exponent $ p_0 >1$ so that for $1<p<p_0$, we have a unique solution of this boundary value problem with the non-tangential maximal function of the gradient of the solution in $L^ p(\\partial\\Omega)$. We also establish the existence of a unique solution when the data is taken from Hardy spaces and Hardy-Sobolev spaces with $ p$ in $(p_1,1]$ for some $p_1 <1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-11-15T16:51:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J25"
    ],
    "keywords": [
      "mixed problem",
      "dimensions",
      "unique solution",
      "non-tangential maximal function",
      "boundary value problem"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Differential Equations",
      "year": 2013,
      "volume": 254,
      "number": 12,
      "pages": 4373
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013JDE...254.4373O"
    }
  }
}