Relaxation of bulk and interfacial energies

Archive for Rational Mechanics and Analysis

Volumn 135, Issue 2, 1996, Pages 107-173

  Barroso, Ana Cristina ^a,b,c   Bouchitté, Guy ^a,b,c   Buttazzo, Giuseppe ^a,b,c   Fonseca, Irene ^a,b,c  

^a CARNEGIE MELLON UNIVERSITY   (United States)

^b UNIVERSITÉ DE TOULON   (France)

^c UNIVERSITY OF PISA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030520244     PISSN: 00039527     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02198453     Document Type: Article

References (44)

1. ALBERTI, G. Rank-one property for derivatives of functions with bounded variation. Proc. Roy. Soc. Edin. A 123 (1993), 239-274.
2. ALMGREM, F., J. TAYLOR & L. WANG. Curvature driven flows: a variational approach. To appear.
3. k). Nonlinear Anal. 23 (1994), 405-425.
4. AMBROSIO, L. & A. BRAIDES, Functional defined on partitions of sets of finite perimeter, I: Integral representation and I-convergence. J. Math. Pure Appl. 69 (1990), 285-305.
5. AMBROSIO, L. & A. BRAIDES. Functional defined on partitions of sets of finite perimeter, II: Semicontinuity, relaxation and homogenization. J. Math. Pures Appl. 69 (1990), 307-333.
6. m) of quasiconvex integrals. J. Funct. Anal. 109 (1992), 76-97.
7. AMBROSIO, L., S. MORTOLA & V. M. TORTORELLI. Functional with linear growth defined on vector valued BV functions. J. Math. Pures Appl. 70 (1991), 269-323.
8. AMBROSIO, L. & E. VIRGA. A boundary value problem for nematic liquid crystals with variable degree of orientation. Arch. Rational Mech. Anal. 114 (1991), 335-347.
9. BALDO, S. Minimal interface criterion for phase transitions in mixtures of Cahn-Hilliard fluids. Ann. Inst. H. Poincaré, Anal. Non Linéaire 7 (1990), 37-65.
10. BARROSO, A. C. & I. FONSECA. Anisotropic singular perturbations. Proc. Roy. Soc. Edin. A 124 (1994), 527-571.
11. BLAKE, A. & A. ZISSERMAN. Visual Reconstruction. MIT Press, Boston, 1987.
12. BOUCHITTÉ, G., A. BRAIDES & G. BUTTAZZO. Relaxation results for some free discontinuity problems. J. Reine Angew. Math. 458 (1995), 1-18.
13. BOUCHITTÉ, G. &G. BUTTAZZO. New lower semicontinuity results for non convex functionals defined on measures. Nonlin. Anal. 15 (1990), 679-692.
14. BOUCHITTÉ, G. & G. BUTTAZZO. Integral representation of nonconvex functionals defined on measures. Ann. Inst. H. Poincaré, Anal. Non Linéaire 9 (1992), 101-117.
15. BOUCHITTÉ, G. & G. BUTTAZZO. Relaxation for a class of nonconvex functionals defined on measures. Ann. Inst. H. Poincaré Anal. Non Linéaire 10 (1993), 345-361.
16. BOUCHITTÉ, G. & G. DAL MASO. Integral representation and relaxation of convex local functionals BV (Ω). Ann. Scuola Norm. Sup. Pisa 20 (1993), 483-533.
17. BRAIDES, A. & A. COSCIA. The interaction between bulk energy and surface energy in multiple integrals. Proc. Royal Soc. Edin. 124A (1994), 737-756.
18. BRAIDES, A. & V. DE CICCO. New lower semicontinuity results for functionals defined on BV. Preprint SISSA (Trieste) 66 (1993).
19. BRAIDES, A. & V. CHIADO PIAT. A derivation formula for integral functionals defined on BV (Ω). Preprint SISSA (Trieste) 144 (1993).
20. BUTTAZZO, G. Semicontinuity, Relaxation and Integral Representation in the Calculus of Variations. Pitman Res. Notes Math. 207. Longman, Harlow, 1989.
21. BUTTAZZO, G. Energies on BV and variational models in fracture mechanics. Preprint Dip. Mat. Univ. Pisa (1994).
22. CELADA, P. & G. DAL MASO, Further remarks on the lower semicontinuity of polyconvex integrals. Ann. Inst. H. Poincaré, Anal. Non Linéaire 11 (1994), 661-691.
23. DACOROGNA, B. Direct Methods in the Calculus of Variations. Springer-Verlag, Berlin, 1989.
24. DAL MASO, G. An Introduction to Γ-Convergence. Birkhäuser, Boston, 1993.
25. DE GIORGI, E. & L. AMBROSIO. Un nuovo tipo di funzionale del calcolo delle variazioni. Atti. Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 82 (1988), 199-210.
26. DE GIORGI, E., M. CARRIERO & A. LEACI. Existence theorem for a minimum problem with free discontinuity set. Arch. Rational Mech. Anal. 108 (1989), 195-218.
27. DE GIORGI, E. & G. LETTA. Une notion générale de convergence faible pour des fonctions croissantes d'ensemble. Ann. Sc. Norm. Sup. Pisa Cl. Sci. 4 (1977), 61-99.
28. EVANS, L. C. & R. F. GARIEPY, Measure Theory and Fine Properties of Functions. CRC Press, 1992.
29. FEDERER, H. Geometric Measure Theory. Springer, 1969.
30. 1,p: a model for the interaction between damage and fracture. Calc. Var. 3 (1995), 407-446.
31. FONSECA, I. & M. KATSOULAKIS. Minimizing movements and mean curvature evolution equations associated to a phase transitions problem. J. Diff. and Int. Eq. 7 (1995), 1619-1656.
32. FONSECA, I. & D. KINDERLEHRER, Lower semicontinuity and relaxation of surface energy functionals. To appear.
33. ∞ of functionals depending on strain and composition. Boundary Value Problems for Partial Differential Equations and Applications, dedicated to Enrico Magenes. J. L. LIONS & C. BAIOCCHI, eds., Masson, Paris, 1993.
34. 1. SIAM J. Math. Anal. 23 (1992), 1081-1098.
35. p) for integrands f(x, u, ∇u). Arch. Rational Mech. Anal. 123 (1993), 1-49.
36. p). Proc. Royal Soc. Edin. 121A (1992), 321-348.
37. GIUSTI, E. Minimal Surfaces and Functions of Bounded Variation. Birkhäuser, Boston, 1984.
38. MORREY, C. B. Quasiconvexity and the semicontinuity of multiple integrals. Pacific J. Math. 2 (1952), 25-53.
39. MORREY, C. B. Multiple Integrals in the Calculus of Variations, Springer-Verlag, Berlin, 1966.
40. MUMFORD, D., & J. SHAH, Boundary detection by minimizing functionals. Proc. IIIE Conf. on Computer Vision and Pattern Recognition, San Francisco, 1985.
41. MUMFORD, D. & J. SHAH, Optimal approximations by piecewise smooth functions and associated variational problems. Comm. Pure Appl. Math. 42 (1989), 577-685.
42. NITZBERG, M., D. MUMFORD & T. SHIOTA. Filtering, Segmentation, and Depth, Lecture Notes in Computer Science, Springer-Verlag, N.Y., 1993.
43. VOL'PERT, A. I. Spaces BV and quasi-linear equations. Math. USSR Sb. 17 (1969), 225-267.
44. ZIEMER, W. P. Weakly Differentiable Functions, Springer-Verlag, Berlin, 1989.