Torus-like Solutions for the Landau-de Gennes Model. Part I: The Lyuksyutov Regime

  title={Torus-like Solutions for the Landau-de Gennes Model. Part I: The Lyuksyutov Regime},
  author={Federico Dipasquale and Vincent Millot and Adriano Pisante},
  journal={Archive for Rational Mechanics and Analysis},
We study global minimizers of a continuum Landau-de Gennes energy functional for nematic liquid crystals, in three-dimensional domains, under a Dirichlet boundary condition. In a relevant range of parameters (which we call the Lyuksyutov regime), the main result establishes the nontrivial topology of the biaxiality sets of minimizers for a large class of boundary conditions including the homeotropic boundary data. To achieve this result, we first study minimizers subject to a physically… 
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  • J. Phys. France
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