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

2021/11/15 by Patricia Bauman, Bauman, Patricia, Daniel R. Phillips +1
Engineering · Mathematics · Physics and Astronomy · #35J50 (Primary) 35J60 (Secondary) #Analysis of PDEs (math.AP) #Black Holes and Theoretical Physics #Elasticity and Material Modeling #FOS: Mathematics #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.2111.08107

openalex publication_date 2021/11/15 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

We investigate minimizers defined on a bounded domain Ω in ℝ² 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 Ω does not intersect the boundary of the constraining set.

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