A nonlocal anisotropic model for phase transitions Part I: The optimal profile problem

Mathematische Annalen

Volumn 310, Issue 3, 1998, Pages 527-560

  Alberti, Giovanni ^a   Bellettini, Giovanni ^b  

^a MAX PLANCK INSTITUTE FOR MATHEMATICS IN THE SCIENCES   (Germany)

^b UNIVERSITY OF PISA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032383890     PISSN: 00255831     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002080050159     Document Type: Article

References (21)

1. G. Alberti, G. Bellettini: A nonlocal anisotropic model for phase transitions, part II: asymptotic behaviour of rescaled energies, to appear.
2. G. Alberti, G. Bellettini, M. Cassandro, E. Presutti: Surface tension in Ising systems with Kac potentials, J. Stat. Phys. 82 (1996), 743-796.
3. 1/2, C. R. Acad. Sci. Paris 319-I (1994), 333-338.
4. A. Baernstein II: A unified approach to symmetrization, in Partial Differential Equations of Elliptic type, pp. 47-91, Cambridge University Press, Cambridge 1994.
5. W. Beckner: Geometric inequalities in Fourier analysis, in Essays on Fourier Analysis in Honor of Elias M. Stein, pp. 36-68, Princeton University Press, Princeton 1995.
6. P.W. Bates, P.C. Fife, X. Ren, X. Wang: Travelling waves in a convolution model for phase transitions, Arch. Rational Mech. & Anal., to appear.
7. F. Brock: A reverse convolution-inequality, J. Convex Anal. 1 (1994), 259-264.
8. F. Brock: Some geometric properties of a nonlocal model for phase transitions, paper in preparation.
9. J.W. Cahn, J.E. Hilliard: Free energy of a nonuniform system I. Interfacial free energy, J. Chem. Phys. 28 (1958) 258-267.
10. A. De Masi, E. Orlandi, E. Presutti, L. Triolo: Motion by curvature by scaling nonlocal evolution equations, J. Stat. Phys. 73 (1993), 543-570.
11. A. De Masi, E. Orlandi, E. Presutti, L. Triolo: Glauber evolution with Kac potentials 1. Mesoscopic and macroscopic limits, interface dynamics, Nonlinearity 7 (1994), 663-696.
12. A. De Masi, E. Orlandi, E. Presutti, L. Triolo: Stability of the interface in a model of phase separation, Proc. Royal Soc. Edinburgh 124-A (1994), 1013-1022.
13. A. De Masi, E. Orlandi, E. Presutti, L. Triolo: Uniqueness and global stability of the instanton in nonlocal evolution equations, Rend. Mat. 14 (1994), 693-723.
14. B. Kawohl: Rearrangements and convexity of level sets in PDE, Lect. Notes in Math. 1150, Springer, Berlin, Heidelberg, New York 1985.
15. M.A. Katsoulakis, P.E. Souganidis: Stochastic Ising model and anisotropi front propagation, J. Stat. Phys. 87 (1997), 63-89.
16. R.C. Rogers: A nonlocal model for the exchange energy in ferromagnetic materials, J. Integral Equations Appl. 3 (1991), 95-127.
17. R.C. Rogers, L. Truskinowsky: Discretization and hysteresis, Physica D, to appear.
18. X. Ren, L. Truskinowsky: paper in preparation.
19. X. Ren, M. Winter: Young measures in a nonlocal phase transition problems, Proc. Royal Soc. Edingburgh, to appear.
20. R.L. Fosdick, D.E. Mason: Single phase energy minimizers for materials with nonlocal spatial dependence, Quart. Appl. Math. 54 (1996), 161-195.
21. R.L. Fosdick, D.E. Mason: On a model of nonlocal continuum mechanics. Part I and II, to appear.