Regularity and the Behavior of Eigenvalues for Minimizers of a Constrained Q-tensor Energy for Liquid Crystals

2015/11/03 by Patricia Bauman, Daniel Phillips, Bauman, Patricia +2 · 1 citation
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Mathematics #Microtubule and mitosis dynamics #math.AP

paper · pdf · doi:10.48550/arxiv.1511.01039

arxiv created 2015/11/03 · openalex publication_date 2015/11/03 · arxiv updated 2015/11/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate minimizers defined on a bounded domain in ℝ² for the Maier--Saupe Q--tensor energy used to characterize nematic liquid crystal configurations. The energy density is singular, as in Ball and Mujamdar's modification of the Ginzburg--Landau Q--tensor model, so as to constrain the competing states to have eigenvalues in the closure of a physically realistic range. We prove that minimizers are regular and in several model problems we are able to use this regularity to prove that minimizers have eigenvalues strictly within the physical range.

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