{
  "id": "0812.3131",
  "version": "v1",
  "published": "2008-12-16T19:12:17.000Z",
  "updated": "2008-12-16T19:12:17.000Z",
  "title": "Landau-De Gennes theory of nematic liquid crystals: the Oseen-Frank limit and beyond",
  "authors": [
    "Apala Majumdar",
    "Arghir Zarnescu"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We study global minimizers of a continuum Landau-De Gennes energy functional for nematic liquid crystals, in three-dimensional domains, subject to uniaxial boundary conditions. We analyze the physically relevant limit of small elastic constant and show that global minimizers converge strongly, in $W^{1,2}$, to a global minimizer predicted by the Oseen-Frank theory for uniaxial nematic liquid crystals with constant order parameter. Moreover, the convergence is uniform in the interior of the domain, away from the singularities of the limiting Oseen-Frank global minimizer. We obtain results on the rate of convergence of the eigenvalues and the regularity of the eigenvectors of the Landau-De Gennes global minimizer. We also study the interplay between biaxiality and uniaxiality in Landau-De Gennes global energy minimizers and obtain estimates for various related quantities such as the biaxiality parameter and the size of admissible strongly biaxial regions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-12-16T19:12:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nematic liquid crystals",
      "landau-de gennes theory",
      "global minimizer",
      "oseen-frank limit",
      "gennes global energy minimizers"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1007/s00205-009-0249-2",
      "journal": "Archive for Rational Mechanics and Analysis",
      "year": 2010,
      "month": "Apr",
      "volume": 196,
      "number": 1,
      "pages": 227
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010ArRMA.196..227M"
    }
  }
}