Calculus of Variations and Geometric Measure Theory

G. Canevari - A. Majumdar - B. Stroffolini

Minimizers of a Landau-de Gennes Energy with a Subquadratic Elastic Energy

created by stroffolini on 06 Jul 2018
modified on 26 Sep 2023


Accepted Paper

Inserted: 6 jul 2018
Last Updated: 26 sep 2023

Journal: Archive for Rational Mechanics and Analysis
Volume: 233
Number: April 2019
Pages: 1169-1210
Year: 2019

ArXiv: 1807.00334 PDF


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.