Calculus of Variations and Geometric Measure Theory
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G. Canevari

Biaxiality in the asymptotic analysis of a 2-D Landau-de Gennes model for liquid crystals

created by canevari on 29 Jan 2021

[BibTeX]

preprint

Inserted: 29 jan 2021

Year: 2013

ArXiv: 1307.8065 PDF

Abstract:

We consider the Landau-de Gennes variational problem on a bound\-ed, two dimensional domain, subject to Dirichlet smooth boundary conditions. We prove that minimizers are maximally biaxial near the singularities, that is, their biaxiality parameter reaches the maximum value $1$. Moreover, we discuss the convergence of minimizers in the vanishing elastic constant limit. Our asymptotic analysis is performed in a general setting, which recovers the Landau-de Gennes problem as a specific case.

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