-
Previous Article
Geometric aspects of transformations of forces acting upon a swimmer in a 3-D incompressible fluid
- DCDS Home
- This Issue
-
Next Article
Dynamics of $\lambda$-continued fractions and $\beta$-shifts
Partial regularity of minimum energy configurations in ferroelectric liquid crystals
1. | Department of Mathematics, Yonsei University, 50 Yonsei-ro, Seadaemun-gu, Seoul 120-749, South Korea |
2. | Department of Mathematics, Chungnam National University, 99 Daehak-ro, Gung-Dong Yuseong-gu, Daejeon 305-764, South Korea |
References:
[1] |
P. Bauman, J. Park and D. Phillips, Existence of solutions to boundary value problems for smectic liquid crystals,, submitted., (). Google Scholar |
[2] |
P. Bauman and D. Phillips, Analysis and stability of bent core liquid crystal fibers,, submitted., (). Google Scholar |
[3] |
G. Carbou, Regularity for critical points of a nonlocal energy,, Calc. Var. Partial Differential Equations, 5 (1997), 409.
|
[4] |
J. Chen and T. Lubensky, Landau-ginzburg mean-field theory for the nematic to smectic C and nematic to smectic A liquid crystal transistions,, Phys. Rev. A, 14 (1976), 1202. Google Scholar |
[5] |
P. G. de Gennes and J. Prost, "The Physics of Liquid Crystals,", Clarendon Press, (1993). Google Scholar |
[6] |
F. C. Frank, On the theory of liquid crystals,, Discuss. Faraday Soc., 25 (1958), 19.
doi: 10.1039/df9582500019. |
[7] |
M. Giaquinta, "Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems,", Princeton University Press, (1983).
|
[8] |
M. Giaquinta, G. Modica and J. Soucek, "Cartesian Currents in the Calculus of Variations II,", Springer, (1998).
|
[9] |
R. Hardt and D. Kinderlehrer, Some regularity results in ferromagnetism,, Commun. in Partial Differential Equations, 25 (2000), 1235.
doi: 10.1080/03605300008821549. |
[10] |
R. Hardt, D. Kinderlehrer and F.-H. Lin, Existence and partial regularity of static liquid crystal configurations,, Comm. Math. Phys., 105 (1986), 547.
doi: 10.1007/BF01238933. |
[11] |
S. T. Lagerwall, "Ferroelectric and Antiferroelectric Liquid Crystals,", Wiley-VCH, (1999). Google Scholar |
[12] |
F. M. Leslie, I. W. Stewart, T. Carlsson and M. Nakagawa, Equivalent smectic C liquid crystal energies,, Continuum Mech. Thermodyn., 3 (1991), 237.
|
[13] |
I. Lukyanchuk, Phase transition between the cholesteric and twist grain boundary C phases,, Phys. Rev. E, 57 (1998), 574.
doi: 10.1103/PhysRevE.57.574. |
[14] |
C. W. Oseen, The theory of liquid crystals,, Trans. Faraday Soc., 29 (1933), 883.
doi: 10.1039/tf9332900883. |
[15] |
M. A. Osipov and S. A. Pikin, Dipolar and quadrupolar ordering in ferroelectric liquid crystals,, J. Phys. II France, 5 (1995), 1223. Google Scholar |
[16] |
J. Park and M. C. Calderer, Analysis of nonlocal electrostatic effects in chiral smectic c liquid crystals,, SIAM J. Appl. Math., 66 (2006), 2107.
doi: 10.1137/050641120. |
[17] |
J. Park, F. Chen and J. Shen, Modeling and simulation of switchings in ferroelectric liquid crystals,, Discrete and Cont. Dyn. Syst., 26 (2010), 1419.
|
[18] |
R. Schoen and K. Uhlenbeck, A regularity theory for harmonic maps,, J. Differential Geom., 17 (1982), 307.
|
[19] |
______, Boundary regularity and the Dirichlet problem for harmonic maps,, J. Differential Geom., 18 (1983), 253.
|
[20] |
L. Simon, "Theorems on Regularity and Singularity of Energy Minimizing Maps,", Birkäuser Verlag, (1996).
|
show all references
References:
[1] |
P. Bauman, J. Park and D. Phillips, Existence of solutions to boundary value problems for smectic liquid crystals,, submitted., (). Google Scholar |
[2] |
P. Bauman and D. Phillips, Analysis and stability of bent core liquid crystal fibers,, submitted., (). Google Scholar |
[3] |
G. Carbou, Regularity for critical points of a nonlocal energy,, Calc. Var. Partial Differential Equations, 5 (1997), 409.
|
[4] |
J. Chen and T. Lubensky, Landau-ginzburg mean-field theory for the nematic to smectic C and nematic to smectic A liquid crystal transistions,, Phys. Rev. A, 14 (1976), 1202. Google Scholar |
[5] |
P. G. de Gennes and J. Prost, "The Physics of Liquid Crystals,", Clarendon Press, (1993). Google Scholar |
[6] |
F. C. Frank, On the theory of liquid crystals,, Discuss. Faraday Soc., 25 (1958), 19.
doi: 10.1039/df9582500019. |
[7] |
M. Giaquinta, "Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems,", Princeton University Press, (1983).
|
[8] |
M. Giaquinta, G. Modica and J. Soucek, "Cartesian Currents in the Calculus of Variations II,", Springer, (1998).
|
[9] |
R. Hardt and D. Kinderlehrer, Some regularity results in ferromagnetism,, Commun. in Partial Differential Equations, 25 (2000), 1235.
doi: 10.1080/03605300008821549. |
[10] |
R. Hardt, D. Kinderlehrer and F.-H. Lin, Existence and partial regularity of static liquid crystal configurations,, Comm. Math. Phys., 105 (1986), 547.
doi: 10.1007/BF01238933. |
[11] |
S. T. Lagerwall, "Ferroelectric and Antiferroelectric Liquid Crystals,", Wiley-VCH, (1999). Google Scholar |
[12] |
F. M. Leslie, I. W. Stewart, T. Carlsson and M. Nakagawa, Equivalent smectic C liquid crystal energies,, Continuum Mech. Thermodyn., 3 (1991), 237.
|
[13] |
I. Lukyanchuk, Phase transition between the cholesteric and twist grain boundary C phases,, Phys. Rev. E, 57 (1998), 574.
doi: 10.1103/PhysRevE.57.574. |
[14] |
C. W. Oseen, The theory of liquid crystals,, Trans. Faraday Soc., 29 (1933), 883.
doi: 10.1039/tf9332900883. |
[15] |
M. A. Osipov and S. A. Pikin, Dipolar and quadrupolar ordering in ferroelectric liquid crystals,, J. Phys. II France, 5 (1995), 1223. Google Scholar |
[16] |
J. Park and M. C. Calderer, Analysis of nonlocal electrostatic effects in chiral smectic c liquid crystals,, SIAM J. Appl. Math., 66 (2006), 2107.
doi: 10.1137/050641120. |
[17] |
J. Park, F. Chen and J. Shen, Modeling and simulation of switchings in ferroelectric liquid crystals,, Discrete and Cont. Dyn. Syst., 26 (2010), 1419.
|
[18] |
R. Schoen and K. Uhlenbeck, A regularity theory for harmonic maps,, J. Differential Geom., 17 (1982), 307.
|
[19] |
______, Boundary regularity and the Dirichlet problem for harmonic maps,, J. Differential Geom., 18 (1983), 253.
|
[20] |
L. Simon, "Theorems on Regularity and Singularity of Energy Minimizing Maps,", Birkäuser Verlag, (1996).
|
[1] |
Luigi C. Berselli, Jishan Fan. Logarithmic and improved regularity criteria for the 3D nematic liquid crystals models, Boussinesq system, and MHD equations in a bounded domain. Communications on Pure & Applied Analysis, 2015, 14 (2) : 637-655. doi: 10.3934/cpaa.2015.14.637 |
[2] |
Hala Ghazi, François James, Hélène Mathis. A nonisothermal thermodynamical model of liquid-vapor interaction with metastability. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2371-2409. doi: 10.3934/dcdsb.2020183 |
[3] |
Alexandre B. Simas, Fábio J. Valentim. $W$-Sobolev spaces: Higher order and regularity. Communications on Pure & Applied Analysis, 2015, 14 (2) : 597-607. doi: 10.3934/cpaa.2015.14.597 |
[4] |
Philippe G. Lefloch, Cristinel Mardare, Sorin Mardare. Isometric immersions into the Minkowski spacetime for Lorentzian manifolds with limited regularity. Discrete & Continuous Dynamical Systems - A, 2009, 23 (1&2) : 341-365. doi: 10.3934/dcds.2009.23.341 |
[5] |
Nhu N. Nguyen, George Yin. Stochastic partial differential equation models for spatially dependent predator-prey equations. Discrete & Continuous Dynamical Systems - B, 2020, 25 (1) : 117-139. doi: 10.3934/dcdsb.2019175 |
[6] |
Bin Pei, Yong Xu, Yuzhen Bai. Convergence of p-th mean in an averaging principle for stochastic partial differential equations driven by fractional Brownian motion. Discrete & Continuous Dynamical Systems - B, 2020, 25 (3) : 1141-1158. doi: 10.3934/dcdsb.2019213 |
[7] |
Changpin Li, Zhiqiang Li. Asymptotic behaviors of solution to partial differential equation with Caputo–Hadamard derivative and fractional Laplacian: Hyperbolic case. Discrete & Continuous Dynamical Systems - S, 2021 doi: 10.3934/dcdss.2021023 |
[8] |
A. Aghajani, S. F. Mottaghi. Regularity of extremal solutions of semilinaer fourth-order elliptic problems with general nonlinearities. Communications on Pure & Applied Analysis, 2018, 17 (3) : 887-898. doi: 10.3934/cpaa.2018044 |
[9] |
Hyeong-Ohk Bae, Hyoungsuk So, Yeonghun Youn. Interior regularity to the steady incompressible shear thinning fluids with non-Standard growth. Networks & Heterogeneous Media, 2018, 13 (3) : 479-491. doi: 10.3934/nhm.2018021 |
2019 Impact Factor: 1.338
Tools
Metrics
Other articles
by authors
[Back to Top]