Minimizers of a Landau–de Gennes energy with a subquadratic elastic energy

Apala Majumdar

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Abstract

We study a modified Landau–de Gennes model for nematic liquid crystals, where the elastic term is assumed to be of subquadratic growth in the gradient. We analyze the behaviour of global minimizers in two- and three-dimensional domains, subject to uniaxial boundary conditions, in the asymptotic regime where the length scale of the defect cores is small compared to the length scale of the domain. We obtain uniform convergence of the minimizers and of their gradients, away from the singularities of the limiting uniaxial map. We also demonstrate the presence of maximally biaxial cores in minimizers on two-dimensional domains, when the temperature is sufficiently low.
Original languageEnglish
Pages (from-to)1169-1210
Number of pages42
JournalArchive for Rational Mechanics and Analysis
Volume233
Issue number3
Early online date1 Apr 2019
DOIs
Publication statusPublished - 1 Sep 2019

ASJC Scopus subject areas

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

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