Hölder 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 mode...

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Bibliographic Details
Published in:Nonlinear analysis 2022-02, Vol.215, p.112641, Article 112641
Main Authors: Canevari, Giacomo, Taylor, Jamie M.
Format: Article
Language:English
Subjects:
Harmonic maps
Landau–de Gennes
Liquid crystals
Oseen–Frank
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Summary: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 Hölder 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.
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2021.112641