Gradient theory of phase transitions in composite media

Royal Society of Edinburgh - Proceedings A

Volumn 133, Issue 2, 2003, Pages 265-296

  Ansini, Nadia ^a   Braides, Andrea ^b   Chiadò Piat, Valeria ^c  

^a UNIVERSITÉ PIERRE ET MARIE CURIE   (France)

^b UNIVERSITY OF ROME TOR VERGATA   (Italy)

^c POLITECNICO DI TORINO   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0037989802     PISSN: 03082105     EISSN: None     Source Type: Journal    
DOI: 10.1017/s0308210500002390     Document Type: Article

References (23)

1. G. Alberti. Variational models for phase transitions, an approach via Γ-convergence. In Calculus of variations and partial differential equations (ed. L. Ambrosio and N. Dancer), pp. 95-114 (Springer, 2000).
2. L. Ambrosio and A. Braides. Functional defined on partitions of sets of finite perimeter. I. Integral representation and Γ-convergence. J. Math. Pures Appl. 69 (1990), 285-305.
3. L. Ambrosio, N. Fusco and D. Pallara. Functions of bounded variation and free discontinuity problems (Oxford University Press, 2000).
4. G. Bouchitté. Convergence et relaxation de fonctionelles du calcul des variations a croissance linéaire. Application a l'homogénéisation en plasticité. Annls Fac. Sci. Toulouse Math. 8 (1986/87), 7-36.
5. p. Arch. Ration. Mech. Analysis 165 (2002), 187-242.
6. A. Braides. Approximation of free-discontinuity problems. Lecture Notes in Mathematics (Springer, 1998).
7. A. Braides. Γ-convergence for beginners (Oxford University Press, 2002)
8. A. Braides and V. Chiadò Piat. A derivation formula for convex integral functionals defined on BV(Ω). J. Convex Analysis 2 (1995), 69-85.
9. m). J. Math. Pures Appl. 75 (1996), 595-626.
10. A. Braides and A. Defranceschi. Homogenization of multiple integrals (Oxford University Press, 1998).
11. J. W. Cahn and J. E. Hilliard. Free energy of a non-uniform system. I. Interfacial free energy. J. Chem. Phys. 28 (1958), 258-267.
12. G. Cortesani. Sequences of non-local functionals which approximate free-discontinuity problems. Arch. Ration. Mech. Analysis 144 (1998), 357-402.
13. G. Dal Maso. An introduction to Γ-convergence (Birkhäuser, 1993).
14. G. Dal Maso and L. Modica. A general theory of variational functionals. In Topics in functional analysis, pp. 149-221 (Pisa: Scuola Normale Superiore Pisa, 1981).
15. H. Federer. Geometric measure theory (Springer, 1968).
16. E. Giusti. Minimal surfaces and functions of bounded variation (Birkhäuser, 1984).
17. M. E. Gurtin. Some results and conjectures in the gradient theory of phase transitions. In Metastability and Incompletely Posed Problems, Proc. Workshop, Minneapolis, MN 1984/85. IMA Vol. Math. Appl. 3 (1987), 135-146.
18. L. Modica. The gradient theory of phase transitions and the minimal interface criterion. Arch. Ration. Mech. Analysis 98 (1987), 123-142.
19. L. Modica and S. Mortola. Un esempio di Γ-convergenza. Boll. UMI B 14 (1977), 285-299.
20. P. Sternberg. The effect of a singular perturbation on nonconvex variational problems. Arch. Ration. Mech. Analysis 101 (1988), 209-260.
21. A. I. Vol'pert. Spaces BV and quasilinear equations. Mat. USSR Sb. 17 (1967), 225-267.
22. V. V. Zhikov, S. K. Kozlov and O. A. Oleinik. Homogenization of differential operators and integral functionals (Springer, 1994).
23. W. P. Ziemer. Weakly differentiate functions (Springer, 1989).