Free Access
Issue |
ESAIM: COCV
Volume 21, Number 1, January-March 2015
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Page(s) | 101 - 137 | |
DOI | https://doi.org/10.1051/cocv/2014025 | |
Published online | 03 December 2014 |
- B.R. Acharya, A. Primak and S. Kumar, Biaxial nematic phase in bent-core thermotropic mesogens. Phys. Rev. Lett. 92 (2004) 145506. [CrossRef] [PubMed] [Google Scholar]
- J.M. Ball and A. Majumdar, Nematic liquid crystals: from Maier–Saupe to a continuum theory. Mol. Cryst. Liq. Cryst. 525 (2010) 1–11. [Google Scholar]
- J.M. Ball and A. Zarnescu, Orientable and non–orientable line field models for uniaxial nematic liquid crystals. Mol. Cryst. Liq. Cryst. 495 (2008) 573–585. [Google Scholar]
- F. Bethuel, Variational Methods for Ginzburg−Landau equations, in Calculus of Variations and Geometric Evolution Problems (Cetraro, 1996). Vol. 1713 of Lect. Notes Math. Springer, Berlin (1999). [Google Scholar]
- F. Bethuel, H. Brezis and F. Hélein, Asymptotics for the minimization of a Ginzburg–Landau functional. Cal. Var. Partial Differ. Equ. 1 (1993) 123–148. [Google Scholar]
- F. Bethuel, H. Brezis and F. Hélein, Ginzburg–Landau Vortices. Birkhäuser, Basel and Boston (1994). [Google Scholar]
- F. Bethuel and T. Rivière, A minimization problem related to superconductivity. Ann. Institut Henri Poincaré, Anal. Non Lin. (1995) 243–303. [Google Scholar]
- H. Campaigne, Partition hypergroups. Amer. J. Math. 6 (1940) 599–612. [CrossRef] [Google Scholar]
- Y. Chen and M. Struwe, Existence and partial regularity results for the heat flow for harmonic maps. Math. Z. Math. Z. 201 (1989) 83–103. [CrossRef] [MathSciNet] [Google Scholar]
- D. Chiron, Étude mathématique de modèles issus de la physique de la matière condensée. PhD thesis, Université Paris VI, France (2004). [Google Scholar]
- A.P. Dietzman, On the multigroups of complete conjugate sets of elements of a group. C.R. (Doklady) Acad. Sci. URSS (N.S.) 49 (1946) 315–317. [Google Scholar]
- G. Di Fratta, J.M. Robbins, V. Slastikov and A. Zarnescu, Profiles of point defects in two dimensions in Landau−de Gennes theory. Preprint (2014) arXiv:1403.2566. [Google Scholar]
- E.C. Gartland and S. Mkaddem, On the local instability of radial hedgehog configurations in nematic liquid crystals under Landau–de Gennes free-energy models. Phys. Rev. E 59 (1999) 563–567. [CrossRef] [Google Scholar]
- D. Golovaty and J.A. Montero, On minimizers of the Landau–de Gennes energy functional on planar domains. Arch. Ration. Mech. Anal. 213 (2014) 447–490. [CrossRef] [Google Scholar]
- R. Hardt, D. Kinderlehrer and F.-H. Lin, Existence and partial regularity of static liquid crystal configurations. Commun. Math. Phys. 105 (1986) 547–570. [CrossRef] [MathSciNet] [Google Scholar]
- D. Henao and A. Majumdar, Symmetry of uniaxial global Landau–de Gennes minimizers in the theory of nematic liquid crystals. J. Math. Anal. 44 (2012) 3217–3241. [CrossRef] [MathSciNet] [Google Scholar]
- R. Ignat, L. Nguyen, V. Slastikov and A. Zarnescu, Stability of the vortex defect in the Landau-de Gennes theory for nematic liquid crystals. C.R. Math. Acad. Sci. Paris 351 (2013) 533–537. [CrossRef] [MathSciNet] [Google Scholar]
- S. Kralj and E.G. Virga, Universal fine structure of nematic hedgehogs. J. Phys. A 34 (2001) 829–838. [CrossRef] [MathSciNet] [Google Scholar]
- S. Kralj, E.G. Virga and S. Žumer, Biaxial torus around nematic point defects. Phys. Rew. E 60 (1999) 1858–1866. [CrossRef] [Google Scholar]
- X. Lamy, Uniaxial symmetry in nematic liquid crystals. Preprint (2014) arXiv:1402.1058. [Google Scholar]
- S. Luckhaus, Convergence of minimizers for the p-Dirichlet integral. Math. Z. 213 (1993) 449–456. [CrossRef] [MathSciNet] [Google Scholar]
- L.A. Madsen, T.J. Dingemans, M. Nakata and E.T. Samulski, Thermotropic biaxial nematic liquid crystals. Phys. Rev. Lett. 92 (2004) 145505. [CrossRef] [PubMed] [Google Scholar]
- A. Majumdar, Equilibrium order parameters of liquid crystals in the Landau–de Gennes theory. Eur. J. Appl. Math. 21 (2010) 181–203. [CrossRef] [Google Scholar]
- A. Majumdar and A. Zarnescu, The Landau−de Gennes theory of nematic liquid crystals: The Oseen–Frank limit and beyond. Arch. Ration. Mech. Anal. 196 (2010) 227–280. [CrossRef] [Google Scholar]
- N.D. Mermin, The topological theory of defects in ordered media. Rev. Modern Phys. 51 (1979) 591–648. [Google Scholar]
- C.B. Morrey, Jr., The problem of Plateau on a Riemannian manifold. Ann. Math. 49 (1948) 807–851. [CrossRef] [Google Scholar]
- R. Moser, Partial Regularity for Harmonic Maps and Related Problems. World Scientific Publishing, Singapore (2005). [Google Scholar]
- N.J. Mottram and C. Newton, Introduction to Q-tensor theory. Research report, Department of Mathematics, University of Strathclyde (2004). [Google Scholar]
- A. Quarteroni, R. Sacco and F. Saleri, Numer. Math. Springer-Verlag, New York (2000). [Google Scholar]
- J. Sacks and K. Uhlenbeck, The existence of minimal immersions of 2-spheres. Ann. Math. 133 (1981) 1–24. [CrossRef] [Google Scholar]
- E. Sandier, Lower bounds for the energy of unit vector fields and applications. J. Funct. Anal. 152 (1998) 379–403. Erratum. Ibidem 171 (2000) 233. [CrossRef] [MathSciNet] [Google Scholar]
- R. Schoen, Analytic aspects of the harmonic map problem, in Seminar on nonlinear partial differential equations, Berkeley, Calif., 1983. Math. Sci. Res. Inst. Publ. Springer, New York (1984). [Google Scholar]
- R. Schoen and K. Uhlenbeck, A regularity theory for harmonic maps. J. Differ. Geometry 17 (1982) 307–33. [Google Scholar]
- N. Schopohl and T.J. Sluckin, Defect core structure in nematic liquid crystals. Phys. Rev. 59 (1987) 2582–2584. [Google Scholar]
- A. Sonnet, A. Killian and S. Hess, Alignment tensor versus director: Description of defects in nematic liquid crystals. Phys. Rev. E 52 (1995) 718–712. [CrossRef] [Google Scholar]
- M. Struwe, On the asymptotic behaviour of the Ginzburg–Landau model in 2 dimensions. J. Differ. Int. Eq. 7 (1994) 1613–1324. Erratum. Ibidem 8 (1995) 224. [Google Scholar]
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