References
1964 [1] M. Krasnoselskii: Positive Solutions of Operator Equations, Noordhoff, Groningen.
1972 [1] P. E. Cladis & M. Kléman: Non-singular Disclinations of Strength S = +1 in Nematics, J. Physique 33, 591–598.
1973 [1] R. B. Meyer: On the Existence of Even Indexed Disclinations in Nematic Liquid Crystals, Phil. Mag. 27, 405–424.
1973 [2] C. E. Williams, P. E. Cladis, & M. Kléman, Screw Disclinations in Nematic Samples with Cylindrical Symmetry, Molec. Crystals and Liquid Crystals 21, 355–373.
1979 [1] W. Jäger & H. Kaul: Uniqueness and Stability of Harmonic Maps and their Jacobi Fields, Manuscripta Math. 28, 269–291.
1981 [1] J. Sacks & K. Uhlenbeck: The Existence of Minimal Immersions of 2-Spheres, Ann. Math. 113, 1–24.
1981 [2] J. Jost: Ein Existenzbeweis für harmonische Abbildungen, die ein Dirichletproblem lösen, mittels der Methode des Wärmeflusses, Manuscripta Math. 34, 17–35.
1983 [1] H. Brezis & J.-M. Coron: Large Solutions for Harmonic Maps in Two Dimensions, Comm. Math. Phys. 92, 203–215.
1983 [2] W. Jäger & H. Kaul: Rotationally Symmetric Harmonic Maps from a Ball into a Sphere and the Regularity Problem for Weak Solutions of Elliptic Systems, J. Reine Angew. Math. 343, 146–161.
1984 [1] R. Schoen: Analytic Aspects of the Harmonic Map Problem, in Seminar on Nonlinear Partial Differential Equations, S. S. Chern ed., MSRI Series vol. 2, Springer-Verlag, 321–350.
1985 [1] M. Struwe: On the evolution of harmonic maps of Riemannian Surfaces, Comm. Math. Helv. 60, 558–581.
1987 [1] H. Brezis & L. Oswald: Singular Solutions for Some Semilinear Elliptic Equations, Arch. Rational Mech. Anal. 99, 249–259.
1989 [1] K. C. Chang: Heat flow and boundary value problems for harmonic maps, Ann. IHP, Analyse Nonlinéaire 6, 363–395.
1990 [1] F. Hélein: Régularité des applications faiblement harmoniques entre une surface et une sphére, C. R. Acad. Sci. Paris 311, 519–524.
1991 [1] T. Rivière & I. Shafrir: Asymptotic analysis of minimizing harmonic maps of regions bounded by two circles, C. R. Acad. Sci. Paris, 313, 503–508.
1991 [2] E. Sandier: Symétrie des applications harmoniques minimisantes d'une couronne vers la sphère, C. R. Acad. Sci. Paris, 313, 435–440.
1991 [3] E. Sandier: Minimisation de l'énergie des cristaux liquides dans un cylindre, C. R. Acad. Sci. Paris, in press.
1992 [1] F. Bethuel, H. Brezis, B. D. Coleman, & F. Hélein: forthcoming.
1992 [2] H. Brezis & L. Nirenberg: Non-Linear Functional Analysis and Applications to Partial Differential Equations, forthcoming.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Bethuel, F., Brezis, H., Coleman, B.D. et al. Bifurcation analysis of minimizing harmonic maps describing the equilibrium of nematic phases between cylinders. Arch. Rational Mech. Anal. 118, 149–168 (1992). https://doi.org/10.1007/BF00375093
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00375093