Torus-like solutions for the Landau-de Gennes model. Part II: Topology of $\mathbb{S}^1$-equivariant minimizers
Federico Dipasquale,
Vincent Millot,
Adriano Pisante
Abstract:We study energy minimization of a continuum Landau-de Gennes energy functional for nematic liquid crystals, in three-dimensional axisymmetric domains and in a restricted class of S 1 -equivariant configurations. We assume smooth and nonvanishing S 1 -equivariant (e.g. homeotropic) Dirichlet boundary conditions and a physically relevant norm constraint (Lyuksyutov constraint) in the interior. Relying on results in [11] in the nonsymmetric setting, we prove partial regularity of minimizers away from a possible f… Show more
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