Uniqueness of planar tangent maps in the modified Ericksen model

2017/06/13 by Onur Alper, Alper, Onur
Mathematics · #49Q20 #58E15 #58E20 #76A15 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:49Q20 #msc:58E15 #msc:58E20 #msc:76A15

paper · pdf · doi:10.48550/arxiv.1706.04098

17 pages

arxiv created 2018/10/14 · arxiv updated 2018/10/16

Abstract

We prove the uniqueness of homogeneous blow-up limits of maps minimizing the modified Ericksen energy for nematic liquid crystals in a planar domain. The proof is based on the Weiss monotonicity formula, and a blow-up argument, originally due to Allard and Almgren \citeAA for minimal surfaces, and L. Simon \citeSL for energy-minimizing maps into analytic targets, which exploits the integrability of certain Jacobi fields.

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