Journal
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
Volume 233, Issue 3, Pages 1169-1210Publisher
SPRINGER
DOI: 10.1007/s00205-019-01376-7
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Funding
- Research-in-Groups program
- Basque Government through the BERC 2018-2021 program
- Spanish Ministry of Economy and Competitiveness [MTM2017-82184-R]
- EPSRC Career Acceleration Fellowship [EP/J001686/1, EP/J001686/2]
- OCIAM Visiting Fellowship
- Keble Advanced Studies Centre
- Project: Variational Advanced TEchniques for compleX MATErials (VATEXMATE) of University Federico II of Naples
- EPSRC [EP/J001686/2] Funding Source: UKRI
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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.
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