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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 language | English |
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Pages (from-to) | 1169-1210 |
Number of pages | 42 |
Journal | Archive for Rational Mechanics and Analysis |
Volume | 233 |
Issue number | 3 |
Early online date | 1 Apr 2019 |
DOIs | |
Publication status | Published - 1 Sept 2019 |
ASJC Scopus subject areas
- Analysis
- Mathematics (miscellaneous)
- Mechanical Engineering
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Dive into the research topics of 'Minimizers of a Landau–de Gennes energy with a subquadratic elastic energy'. Together they form a unique fingerprint.Projects
- 1 Finished
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Fellowship - The Mathematics of Liquid Crystals: Analysis, Computation and Applications
Majumdar, A. (PI)
Engineering and Physical Sciences Research Council
1/08/12 → 30/09/16
Project: Research council