Minimizers of a Landau-de Gennes Energy with a Subquadratic Elastic Energy
| Autor: | Giacomo Canevari, Apala Majumdar, Bianca Stroffolini |
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| Přispěvatelé: | Canevari, G., Majumdar, A., Stroffolini, B. |
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Length scale
Uniform convergence 01 natural sciences Domain (mathematical analysis) Mathematics (miscellaneous) Mathematics - Analysis of PDEs Liquid crystal FOS: Mathematics Landau de Gennes Boundary value problem 0101 mathematics QA Physics Mechanical Engineering 010102 general mathematics Mathematical analysis Elastic energy subquadratic elastic energy 010101 applied mathematics Condensed Matter::Soft Condensed Matter Nematic liquid crystals Landau de Gennes subquadratic elastic energy singularities biaxiality Nematic liquid crystals liquid crystals subquadratic growth regularity of functionals with general growth Gravitational singularity singularities Analysis Energy (signal processing) Analysis of PDEs (math.AP) biaxiality |
| Zdroj: | BIRD: BCAM's Institutional Repository Data instname |
| ISSN: | 1432-0673 |
| Popis: | 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. 42 pages. In this new version, some typos have been fixed |
| Databáze: | OpenAIRE |
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