Defects of liquid crystals with variable degree of orientation

Abstract

We prove that the zero set of a minimizer of the modified Ericksen energy for nematic liquid crystals with variable degree of orientation consists locally of isolated points and a finite union of Hölder continuous curves with only finitely many crossings.

32 pages; minor revisions; typographical errors corrected; new references added

References in corpus (3)

• Rectifiable-Reifenberg and the Regularity of Stationary and Minimizing Harmonic Maps
• Line defects in the small elastic constant limit of a three-dimensional Landau-de Gennes model
• Rectifiability of line defects in liquid crystals with variable degree of orientation

Cited by in corpus (5)

• Nematic-Isotropic phase transition in Liquid crystals: a variational derivation of effective geometric motions
• Disclinations in limiting Landau-de Gennes theory
• A Ginzburg-Landau model with topologically induced free discontinuities
• Rectifiability of line defects in liquid crystals with variable degree of orientation
• A variational singular perturbation problem motivated by Ericksen's model for nematic liquid crystals