Holder regularity and convergence for a non-local model of nematic liquid crystals in the large-domain limit

We consider a non-local free energy functional, modelling a competition between entropy and pairwise interactions reminiscent of the second order virial expansion, with applications to nematic liquid crystals as a particular case. We build on previous work on understanding the behaviour of such models within the large-domain limit, where minimisers converge to minimisers of a quadratic elastic energy with manifold-valued constraint, analogous to harmonic maps. We extend this work to establish Holder bounds for (almost-)minimisers on bounded domains, and demonstrate stronger convergence of (almost)-minimisers away from the singular set of the limit solution. The proof techniques bear analogy with recent work of singularly perturbed energy functionals, in particular in the context of the Ginzburg-Landau and Landau-de Gennes models. (C) 2021 Elsevier Ltd. All rights reserved.

Automated summary

The study investigates a non-local free energy functional that models the competition between entropy and pairwise interactions, with nematic liquid crystals as a specific case. The research extends previous work on the behavior of these models in the large-domain limit to establish Holder bounds for (almost-)minimizers on bounded domains. The proof techniques bear analogy with recent work on singularly perturbed energy functionals, particularly in the context of the Ginzburg-Landau and Landau-de Gennes models.