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The Variety of Configurations of Static Liquid Crystals

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Variational Methods

Part of the book series: Progress in Nonlinear Differential Equations and Their Applications ((PNLDE,volume 4))

Abstract

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.

Research partially supported by the National Science Foundation and the AFOSR through grant DMS-871881.

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Author information

Authors and Affiliations

  1. Mathematics Department, Rice University, Houston, TX, 77251, USA

    Robert Hardt

  2. School of Mathematics, University of Minnesota, Minneapolis, MN, 55455, USA

    David Kinderlehrer

  3. Courant Institute of Mathematical Sciences, New York University, New York, NY, 10012, USA

    Fang Hau Lin

Authors
  1. Robert Hardt
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  2. David Kinderlehrer
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  3. Fang Hau Lin
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Editor information

Editors and Affiliations

  1. Mathématiques, Université Pierre et Marie Curie, 75252, Paris Cedex 05, France

    Henri Berestycki

  2. Département de Mathématiques, Bâtiment 425, Université de Paris-Sud, Centre d’Orsay, 91405, Orsay Cedex, France

    Jean-Michel Coron

  3. CEREMADE, Université de Paris IX-Dauphine, 75775, Paris Cedex 16, France

    Ivar Ekeland

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Hardt, R., Kinderlehrer, D., Lin, F.H. (1990). The Variety of Configurations of Static Liquid Crystals. In: Berestycki, H., Coron, JM., Ekeland, I. (eds) Variational Methods. Progress in Nonlinear Differential Equations and Their Applications, vol 4. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4757-1080-9_9

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  • DOI: https://doi.org/10.1007/978-1-4757-1080-9_9

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4757-1082-3

  • Online ISBN: 978-1-4757-1080-9

  • eBook Packages: Springer Book Archive

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