Open Access
Issue
ESAIM: COCV
Volume 31, 2025
Article Number 47
Number of page(s) 35
DOI https://doi.org/10.1051/cocv/2025032
Published online 04 June 2025
  1. C.W. Oseen, The theory of liquid crystals. Trans. Faraday Soc. 29 (1933) 883–899. [CrossRef] [Google Scholar]
  2. F.C. Frank, On the theory of liquid crystals. Discuss. Faraday Soc. 25 (1958) 19–28. [CrossRef] [Google Scholar]
  3. E.G. Virga, Variational Theories for Liquid Crystals. Vol. 8 of Applied Mathematics and Mathematical Computation. Chapman & Hall, London (1994). [Google Scholar]
  4. J.L. Ericksen, Inequalities in liquid crystal theory. Phys. Fluids 9 (1956) 1205–1207. [Google Scholar]
  5. A. Rapini and M. Papoular, Distorsion d'une lamelle mematique sous champ magnetique conditions d'ancrage aux parois. J. Phys. Colloq. 30 (1969) C4.54–C4.56. [Google Scholar]
  6. J.M. Ball, Mathematics and liquid crystals. Mol. Cryst. Liq. Cryst. 647 (2017) 1–27. [CrossRef] [Google Scholar]
  7. J.M. Ball, Liquid crystals and their defects, in Mathematical Thermodynamics of Complex Fluids. Vol. 2200 of Lecture Notes in Mathematics, edited by E. Feireisl and E. Rocca. Springer, Cham (2017) 1–46. [CrossRef] [Google Scholar]
  8. S. Bedford, Function spaces for liquid crystals. Arch. Ration. Mech. Anal. 219 (2016) 937–984. [CrossRef] [MathSciNet] [Google Scholar]
  9. F.H. Lin and C.C. Poon, On nematic liquid crystal droplets, in Elliptic and Parabolic Methods in Geometry (Minneapolis, MN, (1994). A K Peters, Wellesley, MA (1996) 91–121. [Google Scholar]
  10. Z. Geng and F. Lin, The two-dimensional liquid crystal droplet problem with a tangential boundary condition. Arch. Ration. Mech. Anal. 243 (2022) 1181–1221. [CrossRef] [MathSciNet] [Google Scholar]
  11. G.E. Volovik and O.D. Lavrentovich, Topological dynamics of defects: boojums in nematic drops. Sov. Phys. JETP 58 (1983) 1159–1166. Zh. Eksp. Teor. Fiz. 85(1983) 1997–2010. [Google Scholar]
  12. M. Urbanski, C.G. Reyes, J. Noh, A. Sharma, Y. Geng, V. Subba Rao Jampani and J.P.F. Lagerwall, Liquid crystals in micron-scale droplets, shells and fibers. J. Phys. Condensed Matter 29 (2017) 133003. [CrossRef] [PubMed] [Google Scholar]
  13. P.W. Oakes, J. Viamontes and J.X. Tang, Growth of tactoidal droplets during the first-order isotropic to nematic phase transition of f-actin. Phys. Rev. E 75 (2007) 061902. [CrossRef] [PubMed] [Google Scholar]
  14. K.S. Krishnamurthy, D.S. Shankar Rao, M.B. Kanakala, C.V. Yelamaggad and M. Kleman, Topological defects due to twist-bend nematic drops mimicking colloidal particles in a nematic medium. Soft Matter 16 (2020) 7479–7491. [CrossRef] [PubMed] [Google Scholar]
  15. Y. Li, J. Suen, E. Prince, E. Larin, A. Klinkova, H. Therien-Aubin, B. Yang, A. Helmy, O. Lavrentovich and E. Kumacheva, Colloidal cholesteric liquid crystal in spherical confinement. Nat. Commun. 7 (2016) 12520. [CrossRef] [Google Scholar]
  16. O. Lavrentovich and Y. Nastishin, Division of drops of a liquid crystal in the case of a cholesteric-smectic-a phase transition. Sov. Phys. JETP Lett. 40 (1984) 1015. [Google Scholar]
  17. Y.-K. Kim, S.V. Shiyanovskii and O.D. Lavrentovich, Morphogenesis ofdefects and tactoids during isotropic-nematic phase transition in self-assembled lyotropic chromonic liquid crystals. J. Phys.: Condens. Matter 25 (2013) 404202. [CrossRef] [PubMed] [Google Scholar]
  18. O.D. Lavrentovich, Topological defects in dispersed words and worlds around liquid crystals, or liquid crystal drops. Liquid Cryst. 24 (1998) 117–126. [CrossRef] [Google Scholar]
  19. L. Ambrosio, N. Fusco and D. Pallara, Functions of Bounded Variation and Free Discontinuity Problems. Oxford Mathematical Monographs. The Clarendon Press Oxford University Press, New York (2000). [Google Scholar]
  20. J.M. Ball, G. Canevari and B. Stroffolini, A free discontinuity model for smectic thin films. Liquid Cryst. 50 (2023) 1439–1448. [Google Scholar]
  21. G. Dal Maso, G.A. Francfort and R. Toader, Quasistatic crack growth in nonlinear elasticity. Arch. Ration. Mech. Anal. 176 (2005) 165–225. [Google Scholar]
  22. A. Braides, A. Chambolle and M. Solci, A relaxation result for energies defined on pairs set-function and applications. ESAIM: COCV 13 (2007) 717–734. [CrossRef] [EDP Sciences] [Google Scholar]
  23. L.C. Evans and R.F. Gariepy, Measure Theory and Fine Properties of Functions. Studies in Advanced Mathematics. CRC Press, Boca Raton, FL (1992). [Google Scholar]
  24. G.E. Comi and M. Torres, One-sided approximation of sets of finite perimeter. Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 28 (2017) 181–190. [Google Scholar]
  25. R. Hardt, D. Kinderlehrer and F.-H. Lin, Existence and partial regularity of static liquid crystal configurations. Commun. Math. Phys. 105 (1986) 547–570. [Google Scholar]
  26. D. Bucur and A. Giacomini, Minimization of the k-th eigenvalue of the Robin-Laplacian. J. Funct. Anal. 277 (2019) 643–687. [Google Scholar]
  27. A. Braides and V. Chiadò Piat, Integral representation results for functionals defined on SBV(Ω; Rm). J. Math. Pures Appl. 75 (1996) 595–626. [Google Scholar]
  28. M. Carriero and A. Leaci, Sk-valued maps minimizing the Lp-norm of the gradient with free discontinuities. Ann. Scuola Norm. Sup. Pisa Cl. Sci. 18 (1991) 321–352. [Google Scholar]
  29. S.G. Krantz and H.R. Parks, Distance to Ck hypersurfaces. J. Differ. Equ. 40 (1991) 116–120. [Google Scholar]
  30. T. Schmidt, Strict interior approximation of sets of finite perimeter and functions of bounded variation. Proc. Amer. Math. Soc. 143 (2015) 2069–2084. [Google Scholar]
  31. G. De Philippis and B. Velichkov, Existence and regularity of minimizers for some spectral functionals with perimeter constraint. Appl. Math. Optim. 69 (2014) 199–231. [CrossRef] [MathSciNet] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.