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arXiv · 2111.08107

Regularity of Minimizers for a General Class of Constrained Energies in Two-Dimensional Domains with Applications to Liquid Crystals

Patricia Bauman·Daniel Phillips
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Abstract

We investigate minimizers defined on a bounded domain $\Omega$ in $\mathbb{R}^2$ for singular constrained energy functionals that include Ball and Majumdar's modification of the Landau-de Gennes Q-tensor model for nematic liquid crystals. We prove regularity of minimizers with finite energy and show that their range on compact subdomains of $\Omega$ does not intersect the boundary of the constraining set.

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Patricia Bauman, Daniel Phillips. 2021-11-15. Regularity of Minimizers for a General Class of Constrained Energies in Two-Dimensional Domains with Applications to Liquid Crystals. https://arxiv.org/abs/2111.08107

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