A three-layered minimizer in ℝ2 for a variational problem with a symmetric three-well potential

Communications on Pure and Applied Mathematics

Volumn 49, Issue 7, 1996, Pages 677-715

  Bronsard, Lia ^a   Gui, Changfeng ^c   Schatzman, Michelle ^b  

^a MCMASTER UNIVERSITY   (Canada)

^b UNIVERSITÉ LYON 1   (France)

^c UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0039647010     PISSN: 00103640     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1097-0312(199607)49:7<677::AID-CPA2>3.3.CO;2-6     Document Type: Article

References (23)

1. Abraham, R., and Marsden, J. E., Foundation of Mechanics, 2nd ed., Addison-Wesley, Reading, Mass., 1978.
2. Alikakos, N., and McKinney, W., Remarks on the equilibrium theory for the Cahn-Hilliard equation in one dimension, pp. 75-93 in: Reaction-Diffusion Equations, Edinburgh, 1987-1988, Oxford Sci. Publ., Oxford University Press, New York, 1990.
3. Angenent, S., personal communication.
4. Aronson, D., and Weinberger, H., Nonlinear diffusion in population genetics, combustion and nerve propagation, pp. 5-49 in: Partial Differential Equations and Related Topics, Lecture Notes in Mathematics No. 446, Springer-Verlag, New York, 1975.
5. 2, Arch. Rational Mech. Anal. 126, 1994, pp. 35-58.
6. Bronsard, L., and Kohn, R., On the slowness of phase boundary motion in one space dimension, Comm. Pure Appl. Math. 43, 1990, pp. 983-997.
7. Bronsard L., and Kohn, R., Motion by mean curvature as the singular limit of Ginzburg-Landau dynamics, J. Differential Equations 90, 1991, pp. 211-237.
8. Bronsard, L., and Reitich, F., On three-phase boundary motion and the singular limit of a vector-valued Ginzburg-Landau equation, Arch. Rational Mech. Anal. 124, 1993, pp. 355-379.
9. Chen, X., Generation and propagation of interfaces for reaction-diffusion equations, J. Differential Equations 96, 1992, pp. 116-141.
10. Evans, L. C., Soner, H. M., and Souganidis, P. E., Phase transitions and generalized motion by mean curvature, Comm. Pure Appl. Math. 45, 1992, pp. 1097-1123.
11. Evans, L. C., and Spruck, J., Motion of level sets by mean curvature I, J. Differential Geom. 37, 1991, pp. 635-681.
12. Fife, P., and McLeod, B., The approach of solutions of nonlinear diffusion equation to traveling front solutions, Arch. Rational Mech. Anal. 65, 1977, pp. 335-361.
13. Freidlin, M., Functional Integration and Partial Differential Equations, Princeton University Press, Princeton, 1985.
14. Grant, C., Slow motion in one-dimensional Cahn-Morrel systems, SIAM J. Math. Anal. 26, 1995, pp. 21-34.
15. Ilmanen, T., Convergence of the Allen-Cahn equation to the Brakke's motion by mean curvature, J. Differential Geom. 38, 1993, pp. 417-461.
16. Mottoni, P. de, and Schatzman, M., Evolution géometrique d'interfaces, C. R. Acad. Sci. Paris Sér. I Math. 309, 1989, pp. 453-458.
17. Mottoni, P. de, and Schatzman, M., Geometrical evolution of developed interfaces, Trans. Amer. Math. Soc. 347, 1995, pp. 1533-1589.
18. Mullins, W., Two-dimensional motion of idealized grain boundaries, J. Appl. Phys. 27, 1956, pp. 900-904.
19. Mullins, W., On idealized two-dimensional grain growth, Scripta Metall. 22, 1988, pp. 1441-1444.
20. Rubinstein, J., Sternberg, P., and Keller, J., Fast reaction, slow diffusion, and curve shortening, SIAM J. Appl. Math. 49, 1989, pp. 116-133.
21. Sternberg, P., Vector-valued local minimizers of nonconvex variational problems, Rocky Mountain J. Math. 21, 1991, pp. 799-807.
22. Sternberg, P., and Ziemer, W., Local minimizers of a three-phase partition problem with triple junction, Proc. Roy. Soc. Edinburgh Sect. A 124, 1994, pp. 1059-1073.
23. Woodruff, D., The solid-liquid interface, Cambridge University Press, 1973.