Advertisement

A mathematical afterthought

  • David Kinderlehrer
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1063)

Keywords

Liquid Crystal Nematic Liquid Crystal Kinematic Variable Liquid Crystal Phase Liquid Crystal Polymer 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Aifantis, E. and J. Serrin, Toward a mechanical theory of phase transformation. Corrosion Center technical report, U. of M., (1980).Google Scholar
  2. 2.
    Aubert, G. and R. Tahraoni, Théorèmes d’existence pour problèmes du calcul des variations, J. Diff. Eq. 33 (1979), 1–15.CrossRefGoogle Scholar
  3. 3.
    Courant, R. and D. Hilbert, Methods of Mathematical Physics, Vol. I, Wiley (New York), 1962.Google Scholar
  4. 4.
    Dacorogna, B., A relaxation theorem and its application to the equilibrium of gases, Arch. Rat. Mech. Anal.Google Scholar
  5. 5.
    Dafermos, C., The second law of thermodynamics and stability, Arch. Rat. Mech. Anal. 70 (1979), 167–179.CrossRefGoogle Scholar
  6. 6.
    Diaz, J.-P., Sur les équations d’évolution d’un nématique incompressible soumis à l’action d’un champ magnétique homogène, C.R.A.S. Paris, Série A., 282 (1976), 71–74.Google Scholar
  7. 7.
    _____, Un système d’équations en rapport avec les équations d’évolution bidimensionelles d’un liquide nématique, J. mécanique 15 (1976), 697–709.Google Scholar
  8. 8.
    _____, Sur l’existence et unicité de solutions d’un modèle approxime des équations d’évolution tridimensionelles d’un cristal liquide nématique, Ann. S.N.S. Pisa, 5.1 (1978), 1–13.Google Scholar
  9. 9.
    Ekeland, I and R. Temam, Convex Analysis and Variational Problems, North Holland (1976).Google Scholar
  10. 10.
    Ericksen, J., Equilibrium theory of liquid crystals, Advances in Liquid Crystals, (ed. Glenn Brown) 2 (1976), 233–298.CrossRefGoogle Scholar
  11. 11.
    _____, Equilibrium of bars, J. Elast. 5 (1975), 191–202.CrossRefGoogle Scholar
  12. 12.
    Fosdick, R.L. and G. MacSithigh, Helical shear of an elastic circular tube with a nonconvex stored energy (preprint).Google Scholar
  13. 13.
    Gurtin, M. and R. Temam, On the antiplane shear problem in finite elasticity, J. Elast. 11 (1981).Google Scholar
  14. 14.
    Hagan, Dynamic phase transitions, Ph.D. Thesis, Dept. of Math. Sciences, Rensselaer Polytechnic Institute, Troy, NY (1982).Google Scholar
  15. 15.
    Hardt, R. and D. Kinderlehrer, Elastic plastic deformation, Appl. Math. Opt. 10 (1983), 203–246.CrossRefGoogle Scholar
  16. 16.
    Leslie, F.M., Theory of flow phenomena in liquid crystals, Advances in Liquid Crystals (ed. Glenn Brown) 4, 1–81.Google Scholar
  17. 17.
    Marcellini, P. Alcune osservazioni sull’esistenza del minimo di integrali del calcolo delle variazioni senza ipotesi di convessita, Rend. Math. 13 (1980), 271–281.Google Scholar
  18. 18.
    _____, A relation between existence of minima for nonconvex integrals and uniqueness for non strictly convex integrals of calculus of variations, Proc. Cong. Math. Theories Opt., S. Margh. Lig. (1981).Google Scholar
  19. 19.
    Mascolo, E. and R. Schianchi, Existence theorems for non convex problems, J. Math. Pures et Appl. (to appear).Google Scholar
  20. 20.
    _____, Further remarks on nonconvex problems (preprint).Google Scholar
  21. 21.
    Renardy, M., A local existence and uniqueness theorem for a K-BKZ fluid, Univ. of Wisc. MRC technical summary 2530.Google Scholar
  22. 22.
    Slemrod, M., Admissibility criteria for propagating phase boundaries in a van der Waals fluid, Arch. Rat. Mech. and Anal. 81 (1983) 301–315.CrossRefGoogle Scholar
  23. 23.
    Spector, S., On the absence of bifurcation for elastic bars in uniaxial tension, I.M.A. preprint 25, (1983).Google Scholar

Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • David Kinderlehrer
    • 1
  1. 1.School of MathematicsUniversity of MinnesotaMinneapolis

Personalised recommendations