Calculus of Variations and Geometric Measure Theory
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G. Canevari - J. M. Taylor

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

created by canevari on 29 Jan 2021
modified on 26 May 2021

[BibTeX]

preprint

Inserted: 29 jan 2021
Last Updated: 26 may 2021

Year: 2021

ArXiv: 2101.10288 PDF

Abstract:

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 H\"older 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.

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