The Variety of Configurations of Static Liquid Crystals

  • Robert Hardt
  • David Kinderlehrer
  • Fang Hau Lin
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 4)


Here we make several observations on a variety of special classes of harmonic maps from domains in IR3 to S 2. Such maps are relevant for the study of liquid crystals; see e.g. [HK1], [HKL1], [HKLu]. Part of our work is motivated by questions about the nonuniqueness and the number of harmonic maps having fixed boundary data. Here we show that the number may actually be infinite. For example, by Corollary 3.2 below there exists a one parameter family of distinct energy-minimizers each having the same Dirichlet boundary data.


Liquid Crystal Singular Point Boundary Data Minimal Hypersurface Monotonicity Formula 
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Copyright information

© Springer Science+Business Media New York 1990

Authors and Affiliations

  • Robert Hardt
    • 1
  • David Kinderlehrer
    • 2
  • Fang Hau Lin
    • 3
  1. 1.Mathematics DepartmentRice UniversityHoustonUSA
  2. 2.School of MathematicsUniversity of MinnesotaMinneapolisUSA
  3. 3.Courant Institute of Mathematical SciencesNew York UniversityNew YorkUSA

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