Free Access
Volume 10, Number 1, January 2004
Page(s) 142 - 167
Published online 15 February 2004
  1. F. Alouges, A new algorithm for computing liquid crystal stable configurations: the harmonic mapping case. SIAM J. Numer. Anal. 34 (1997) 1708–1726. [Google Scholar]
  2. F. Alouges and B.D. Coleman, Numerical bifurcation of equilibria of nematic crystals between non-co-axial cylinders. Math. Models Methods Appl. Sci. 11 (2001) 459–473. [Google Scholar]
  3. D. Braess, Finite elements, in Theory, fast solvers, and applications in solid mechanics. Translated from the 1992 German edition by Larry L. Schumaker. Cambridge University Press, Cambridge, 2nd edn. (2001). [Google Scholar]
  4. H. Brézis, Analyse fonctionnelle. Masson (1996). [Google Scholar]
  5. H. Brézis and J.-M. Coron, Large solutions for harmonic maps in two dimensions. Comm. Math. Phys. 92 (1983) 203–215. [Google Scholar]
  6. K.-C. Chang, W.-Y. Ding and R. Ye, Finite-time blow up of the heat flow of harmonic maps from surfaces. J. Differ. Geom. 36 (1992) 507–515. [Google Scholar]
  7. P.G. Ciarlet, Introduction à l'analyse numérique matricielle et à l'optimisation. Masson (1988). [Google Scholar]
  8. P.-G. De Gennes and J. Prost, The physics of liquid crystals. Clarendon Press, Oxford (1993). [Google Scholar]
  9. R. Fletcher and C.M. Reeves, Function minimization by conjugate gradients. Comput. J. 7 (1994) 149–154. [Google Scholar]
  10. M. Giaquinta, G. Modica and J. Souček, Cartesian currents in the calculus of variations. I. Springer-Verlag, Berlin (1998). [Google Scholar]
  11. M. Giaquinta, G. Modica and J. Souček, Cartesian currents in the calculus of variations. II. Springer-Verlag, Berlin (1998). [Google Scholar]
  12. R.M. Hardt, Singularities of harmonic maps. Bull. Amer. Math. Soc. (N.S.) 34 (1997) 15–34. [Google Scholar]
  13. E. Hebey, Introduction à l'analyse non linéaire sur les variétés. Diderot Editeur Arts et Sciences (1987). [Google Scholar]
  14. F. Hélein, Régularité des applications faiblement harmoniques entre une surface et une sphère. C. R. Acad. Sci. Paris Sér. I Math. 311 (1990) 519–524. [Google Scholar]
  15. F. Hélein, Symétries dans les problèmes variationnels et applications harmoniques. Istituti Editoriali e Poligrafici Internazionali, Pisa-Roma (1998). [Google Scholar]
  16. J. Jost, Harmonic mappings betwenn surfaces. Springer-verlag, Lecture Notes in Math. 1062 (1984). [Google Scholar]
  17. W.P.A Klingenberg, Riemannian Geometry. Walter de Gruyter (1995). [Google Scholar]
  18. E. Kuwert, Minimizing the energy of maps from a surface into a 2-sphere with prescribed degree and boundary values. Manuscripta Math. 83 (1994) 31–38. [Google Scholar]
  19. L. Lemaire, Applications harmoniques de surfaces riemanniennes. J. Differ. Geom. 13 (1978) 51–78. [Google Scholar]
  20. A. Lichnewsky, Une méthode de gradient conjugué sur des variétés : application à certains problèmes de valeurs propres non linéaires. Numer. Funct. Anal. Optim. 1 (1979) 515–560. [Google Scholar]
  21. P.L. Lions, The concentration-compactness principle in the calculus of variations. The limit case, part 2. Rev. Mat. Iberoamericana 1 (1985) 45–121. [Google Scholar]
  22. C.B. Morrey, Multiple integrals in the calculus of variations. Springer, New York (1966). [Google Scholar]
  23. J.W. Neuberger, Sobolev gradients and boundary conditions for partial differential equations, in Recent developments in optimization theory and nonlinear analysis (Jerusalem, 1995), Amer. Math. Soc., Providence, RI. Contemp. Math. 204 (1997) 171–181 [Google Scholar]
  24. E. Polak, Optimization, Appl. Math. Sci. 124 (1997). [Google Scholar]
  25. J. Qing, Remark on the Dirichlet problem for harmonic maps from the disc into the 2-sphere. Proc. R. Soc. Edinb. 122A (1992) 63–67. [Google Scholar]
  26. J. Qing, Boundary regularity of weakly harmonic maps from surfaces. J. Funct. Anal. 114 (1993) 63–67. [Google Scholar]
  27. R. Schoen and K. Uhlenbeck, Boundary regularity and the Dirichlet problem for harmonic maps. J. Dif. Geom. 18 (1983) 253–268. [Google Scholar]
  28. J.R. Shewchuk, Triangle: engineering a 2d quality mesh generator and delaunay triangulator. [Google Scholar]
  29. J.R. Shewchuk, An introduction to the conjugate gradient method without the agonizing pain. (1994). [Google Scholar]
  30. A. Soyeur, The Dirichlet problem for harmonic maps from the disc into the 2-sphere. Proc. R. Soc. Edinb. 113A (1989) 229–234. [Google Scholar]

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