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On Variational Aspects of the Theory of Liquid Crystals with Variable Degree of Orientation

  • Z. Naniewicz
  • P. D. Panagiotopoulos
Conference paper
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 66)

Abstract

Let us consider a nematic liquid crystal occupying in the three dimensional Euclidean space R 3 a bounded region Ω with Lipschitz continuous boundary ∂Ω. We put ourselves into the framework of Ericksen’s theory of nematic liquid crystals with variable degree of orientation ([3], see also [4], p. 331) and we assume that the crystal is determined by the orientation vector n : Ω → R 3 with n = 1 and the degree of orientation s : Ω → [-1/2, 1 ]. The Prank energy functional F E in a setting of the one constant approximation is given by where ∇ = (∂ j ) stands for the gradient operator, k E and k are positive module, σ0 : Ω → R is De Gennes potential of the form with positive constants a, b, c and d.

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References

  1. Ambrosio, L. (1990) Existence of Minimal Energy Configurations of Nematic Liquid Crystals with Variable Degree of Orientation, Manuscripta Math. 68 215–228.MathSciNetCrossRefzbMATHGoogle Scholar
  2. Lin, F.H. (1991) On Nematic Liquid Crystals with Variable Degree of Orientation, Comm. Pure Appl. Math. XLIV 453–468.CrossRefGoogle Scholar
  3. Ericksen, J.L. (1991) Liquid Crystals with Variable Degree of Orientation, Arch. Rational Mech. Anal. 113 97–120.MathSciNetADSCrossRefzbMATHGoogle Scholar
  4. Virga, E.G. (1994) Variational Theories for Liquid Crystals, Chapman & Hall London.zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1999

Authors and Affiliations

  • Z. Naniewicz
    • 1
    • 2
  • P. D. Panagiotopoulos
    • 3
  1. 1.Aristotle University of Thessaloniki, Department of Civil EngineeringThessalonikiGreece
  2. 2.Institute of Applied Mathematics and MechanicsWarsawPoland
  3. 3.Faculty of Mathematics and PhysicsRWTHAachenGermany

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