Keywords
- Liquid Crystal
- Nematic Liquid Crystal
- Regularity Theory
- Nonlinear Elliptic System
- Fractional Step Method
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
F. Bethuel and X. Zheng, Sur la densité des fonctions régulières entre deux variétés dans des espaces de Sobolev, CRAS Paris, 303, (1986), 447–449.
H. Brezis, J. M. Coron and E. Lieb, Estimations d’énergie pour des applications de R3 a valeurs dans S2, CRAS Paris, 303, (1986), 207–210.
H. Brezis, J. M. Coron and E. Lieb, Harmonic maps with defects, IMA preprint 253, to appear, Comm. Math. Physics.
W. Brinkman and P. Cladis, Defects in liquid crystals, Physics Today, May 1982, 48–54.
S. Campanato, Sistemi ellitici in forma divergenza. Regolarità all’interno, Quaderni della SNS Pisa (1980).
S. Chandrasekhar, Liquid Crystals, Cambridge (1977).
R. Cohen, R. Hardt, D. Kinderlehrer, S.-Y. Lin and M. Luskin, Minimum energy configurations for liquid crystals: computational results, Theory and applications of liquid crystals, IMA Volumes in math. and appl. 5 (J.L. Ericksen and D. Kinderlehrer, eds.).
P. G. de Gennes, The physics of liquid crystals, Oxford (1974).
J. L. Ericksen, Equilibrium theory of liquid crystals, Adv. in liquid crystals 2, (G. H. Brown, ed.) Academic Press (1976), 233–298.
J. L. Ericksen, Nilpotent energies in liquid crystal theory, Arch. Rat. Mech. Anal. 10 (1962), 189–196.
J. L. Ericksen and D. Kinderlehrer, Theory and application of liquid crystals, IMA Volumes in math. and appl. 5.
F. W. Gehring, The LP integrability of the partial derivatives of a conformal mapping, Acta Math. 130 (1973), 55–72.
M. Giaquinta, Multiple integrals in the calculus of variations and nonlinear elliptic systems, Annals of Math. Studies 105, Princeton, 1983.
R. Hardt and D. Kinderlehrer, Mathematical questions of liquid crystal theory, Theory and application of liquid crystals, IMA Volumes in math. and appl. 5 (J.L. Ericksen and D. Kinderlehrer, eds.) (1987).
R. Hardt, D. Kinderlehrer and F.-H. Lin, Existence et régularité des configurations statiques des cristaux liquides, CRAS Paris 301, (1985), 577–579.
R. Hardt, D. Kinderlehrer and F.-H. Lin, Existence and partial regularity of static liquid crystal configurations, IMA preprint 175, Comm. Math. Physics 105 (1986), 547–570.
R. Hardt, D. Kinderlehrer and F.-H. Lin, A remark about the stability of smooth equilibrium configurations of static liquid crystals, IMA preprint 231, Mol. Cryst Liq. Cryst. 136 (1986).
R. Hardt, D. Kinderlehrer and F.-H. Lin, to appear.
R. Hardt, D. Kinderlehrer and F.-H. Lin, to appear.
R. Hardt and F.-H. Lin, A remark on H1 mappings, Manus. math. 56, (1986), 1–10.
R. Hardt and F.-H. Lin, Mappings that minimize the p th power of the gradient, to appear.
F. Leslie, Theory of flow phenomena in liquid crystals, Adv. Liq. Cryst. 4 (G. H. Brown, ed.) Academic Press (1979), 1–81.
F. Leslie, Theory of flow phenomena in nematic liquid crystals, Theory and application of liquid crystals, IMA Volumes in math. and appl. 5, (J.L. Ericksen and D. Kinderlehrer, eds.) (1987).
E. MacMillan, The statics of liquid crystals, Thesis, Master of Science, The Johns Hopkins University, 1982.
N. G. Meyers and A. Elcrat, Some results on regularity for solutions of nonlinear elliptic systems and quasiregular functions, Duke Math J. 42 (1975), 121–136.
R. Schoen and K. Uhlenbeck, A regularity theory for harmonic maps, J. Diff. Geometry 17 (1982), 307–335.
C. Williams, P. Pieranski and P. E. Cladis, Nonsingular S=+1 screw disclination lines in nematics, Phys. Rev. Letters 29 (1972), 90–92.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Additional information
Dedicated to Hans Lewy
Rights and permissions
Copyright information
© 1988 Springer-Verlag
About this paper
Cite this paper
Hardt, R., Kinderlehrer, D., Luskin, M. (1988). Remarks about the mathematical theory of liquid crystals. In: Hildebrandt, S., Kinderlehrer, D., Miranda, M. (eds) Calculus of Variations and Partial Differential Equations. Lecture Notes in Mathematics, vol 1340. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0082891
Download citation
DOI: https://doi.org/10.1007/BFb0082891
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-50119-0
Online ISBN: 978-3-540-45932-3
eBook Packages: Springer Book Archive
