{
  "id": "1808.00611",
  "version": "v1",
  "published": "2018-08-02T00:36:14.000Z",
  "updated": "2018-08-02T00:36:14.000Z",
  "title": "Embeddings for the space $LD_γ^{p}$ on sets of finite perimeter",
  "authors": [
    "Nikolai V. Chemetov",
    "Anna L. Mazzucato"
  ],
  "comment": "20 pages, 3 figures",
  "categories": [
    "math.AP"
  ],
  "abstract": "Given an open set with finite perimeter $\\Omega\\subset \\mathbb{R}^n$, we consider the space $LD_\\gamma^{p}(\\Omega)$, $1\\leq p<\\infty$, of functions with $p$th-integrable deformation tensor on $\\Omega$ and with $p$ th-integrable trace value on the essential boundary of $\\Omega$. We establish the continuous embedding $LD_\\gamma^{p}(\\Omega)\\subset L^{pN/(N-1)}(\\Omega)$. The space $LD_\\gamma^{p}(\\Omega)$ and this embedding arise naturally in studying the motion of rigid bodies in a viscous, incompressible fluid.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-08-02T00:36:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E35",
      "74F10"
    ],
    "keywords": [
      "finite perimeter",
      "open set",
      "th-integrable trace value",
      "rigid bodies",
      "essential boundary"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}