A lower semicontinuity result in SBD

Journal of Convex Analysis

Volumn 15, Issue 1, 2008, Pages 191-200

  Gargiulo, Giuliano ^a   Zappale, Elvira ^b  

^a UNIVERSITY OF SANNIO   (Italy)

^b UNIVERSITY OF SALERNO   (Italy)

Author keywords

Convexity; Fracture; Lower semicontinuity; Special functions of bounded deformation; Subadditivity

Indexed keywords

EID: 39749145139     PISSN: 09446532     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (19)

1. L. Ambrosio: A compactness theorem for a new class of functions of bounded variation, Boll. Unione Mat. Ital., VII. Ser., B 3 (1989) 857-881.
2. L. Ambrosio: Existence theory for a new class of variational problems, Arch. Ration. Mech. Anal. 111 (1990) 291-322.
3. L. Ambrosio, A. Braides: Functional denned on partitions in sets of finite perimeter I: Integral representation and Γ convergence, J. Math. Pures Appl., IX. Ser. 69 (1990) 285-306.
4. L. Ambrosio, A. Braides: Functional defined on partitions in sets of finite perimeter II: semicontinuity, relaxation, homogenization, J. Math. Pures Appl., IX. Sér. 69 (1990) 307-333.
5. L. Ambrosio, A. Coscia, G. Dal Maso, Fine properties of functions with bounded deformation, Arch. Ration. Mech. Anal. 139 (1997) 201-238.
6. L. Ambrosio, N. Fusco, D. Pallara: Functions of Bounded Variation and Free Discontinuity Problems, Clarendon Press, Oxford (2000).
7. G. I. Barenblatt: The mathematical theory of equilibrium craks in brittle fracture, Adv. Appl. Mech. 7 (1962) 55-129.
8. G. Bellettini, A. Coscia, G. Dal Maso: Compactness and lower semicontinuity in SBD(Ω), Math. Z. 228 (1998) 337-351.
9. G. Buttazzo: Semicontinuity, Relaxation and Integral Representation in the Calculus of Variations, Pitman Res. Notes Math. Ser. 207, Longman Scientific &. Technical, Harlow (1989).
10. E. De Giorgi, L. Ambrosio: Un nuovo tipo di funzionale del calcolo delle variazioni, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 82(8) (1998) 199-210.
11. F. Ebobisse: A lower semicontinuity result for some integral functionals in the space SBD, Nonlinear Anal., Theory Methods Appl. 62A(7) (2005) 1333-1351.
12. C. Evans, R. Gariepy: Measure Theory and Fine Properties of Functions, Studies in Advanced Mathematics, CRC Press, Boca Raton (1992).
13. H. Federer: Geometric Measure Theory, Springer, Berlin (1969).
14. A. Griffith: The phenomena of rupture and flows in solids, Phil. Trans. Roy. Soc. London A 221 (1920) 163-198.
15. W. S. Loud: Periodic solutions of x″ + cx′ + g(x) = εf(t), Mem. Am. Math. Soc. 31 (1959).
16. R. T. Rockafellar: Convex Analysis, Princeton University Press, Princeton (1970).
17. R. Temam: Problémes Mathématiques en Plasticité, Gauthiers-Villars, Paris (1983).
18. R. Temam, G. Strang: Functions of bounded deformation, Arch. Ration. Mech. Anal. 75 (1980) 7-21.
19. W. P. Ziemer: Weakly differentiable functions. Sobolev spaces and functions of bounded variation, Springer, Berlin (1989).