Skip to main content

A mathematical afterthought

  • Conference paper
  • First Online:
Orienting Polymers

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1063))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 29.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 39.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aifantis, E. and J. Serrin, Toward a mechanical theory of phase transformation. Corrosion Center technical report, U. of M., (1980).

    Google Scholar 

  2. Aubert, G. and R. Tahraoni, Théorèmes d’existence pour problèmes du calcul des variations, J. Diff. Eq. 33 (1979), 1–15.

    Article  Google Scholar 

  3. Courant, R. and D. Hilbert, Methods of Mathematical Physics, Vol. I, Wiley (New York), 1962.

    Google Scholar 

  4. Dacorogna, B., A relaxation theorem and its application to the equilibrium of gases, Arch. Rat. Mech. Anal.

    Google Scholar 

  5. Dafermos, C., The second law of thermodynamics and stability, Arch. Rat. Mech. Anal. 70 (1979), 167–179.

    Article  Google Scholar 

  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. _____, 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. _____, 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. Ekeland, I and R. Temam, Convex Analysis and Variational Problems, North Holland (1976).

    Google Scholar 

  10. Ericksen, J., Equilibrium theory of liquid crystals, Advances in Liquid Crystals, (ed. Glenn Brown) 2 (1976), 233–298.

    Article  CAS  Google Scholar 

  11. _____, Equilibrium of bars, J. Elast. 5 (1975), 191–202.

    Article  Google Scholar 

  12. Fosdick, R.L. and G. MacSithigh, Helical shear of an elastic circular tube with a nonconvex stored energy (preprint).

    Google Scholar 

  13. Gurtin, M. and R. Temam, On the antiplane shear problem in finite elasticity, J. Elast. 11 (1981).

    Google Scholar 

  14. Hagan, Dynamic phase transitions, Ph.D. Thesis, Dept. of Math. Sciences, Rensselaer Polytechnic Institute, Troy, NY (1982).

    Google Scholar 

  15. Hardt, R. and D. Kinderlehrer, Elastic plastic deformation, Appl. Math. Opt. 10 (1983), 203–246.

    Article  Google Scholar 

  16. Leslie, F.M., Theory of flow phenomena in liquid crystals, Advances in Liquid Crystals (ed. Glenn Brown) 4, 1–81.

    Google Scholar 

  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. _____, 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. Mascolo, E. and R. Schianchi, Existence theorems for non convex problems, J. Math. Pures et Appl. (to appear).

    Google Scholar 

  20. _____, Further remarks on nonconvex problems (preprint).

    Google Scholar 

  21. Renardy, M., A local existence and uniqueness theorem for a K-BKZ fluid, Univ. of Wisc. MRC technical summary 2530.

    Google Scholar 

  22. Slemrod, M., Admissibility criteria for propagating phase boundaries in a van der Waals fluid, Arch. Rat. Mech. and Anal. 81 (1983) 301–315.

    Article  Google Scholar 

  23. Spector, S., On the absence of bifurcation for elastic bars in uniaxial tension, I.M.A. preprint 25, (1983).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Jerald L. Ericksen

Rights and permissions

Reprints and permissions

Copyright information

© 1984 Springer-Verlag

About this paper

Cite this paper

Kinderlehrer, D. (1984). A mathematical afterthought. In: Ericksen, J.L. (eds) Orienting Polymers. Lecture Notes in Mathematics, vol 1063. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072156

Download citation

  • DOI: https://doi.org/10.1007/BFb0072156

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13340-7

  • Online ISBN: 978-3-540-38869-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics