On Minimizers of the Landau-de Gennes Energy Functional on Planar Domains

Abstract

We study tensor-valued minimizers of the Landau-de Gennes energy functional on a simply-connected planar domain $\Omega$ with non-contractible boundary data. Here the tensorial field represents the second moment of a local orientational distribution of rod-like molecules of a nematic liquid crystal. Under the assumption that the energy depends on a single parameter---a dimensionless elastic constant $\eps>0$---we establish that, as $\eps\to0$, the minimizers converge to a projection-valued map that minimizes the Dirichlet integral away from a single point in $\Omega$. We also provide a description of the limiting map.

References in corpus (2)

• Introduction to Q-tensor theory
• Equilibrium order parameters of liquid crystals in the Landau-De Gennes theory

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