Free-discontinuity problems via functionals involving the L1-norm of the gradient and their approximations

Interfaces and Free Boundaries

Volumn 1, Issue 1, 1999, Pages 17-37

  Alicandro, Roberto ^a   Braides, Andrea ^a   Shah, Jayant ^b  

^a SISSA   (Italy)

^b NORTHEASTERN UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0002622913     PISSN: 14639963     EISSN: None     Source Type: Journal    
DOI: 10.4171/IFB/2     Document Type: Article

References (22)

1. AMBROSIO, L. A compactness theorem for a new class of functions of bounded variation. Boll. Un. Mat. Ital. 3-B, (1989) 857-881.
2. AMBROSIO, L. & BRAIDES, A. Energies in SBV and variational models in fracture mechanics. in CIORANESCU, D., damlamian, A., & Donato, P. (eds), Homogenization and Applications to Material Sciences, pp. 1-22. GAKUTO, Gakkótosho, Tokyo, Japan (1997).
3. AMBROSIO, L. & TORTORELLI, V. M. Approximation of functional depending on jumps by elliptic functionals via Γ-convergence. Comm. Pure Appl. Math. 43, (1990) 999-1036.
4. AMBROSIO, L. & TORTORELLI, V. M. On the approximation of free-discontinuity problems. Boll. Un. Mat. Ital. 6-B, (1992) 105-123.
5. AMBROSIO, L., FUSCO, N., & PALLARA, D. Special Functions of Bounded Variation and Free Discontinuity Problems. Oxford University Press, Oxford, to appear.
6. BARENBLATT, G. I. The mathematical theory of equilibrium cracks in brittle fracture. Adv. Appl. Mech. 7, (1962) 55-129.
7. BOUCHITTÉ, G., BRAIDES, A., & BUTTAZZO, G. Relaxation results for some free discontinuity problems. J. Reine Angew. Math. 458, (1995) 1-18.
8. BRAIDES. A. Approximation of Free-discontinuity Problems. Lecture Notes in Mathematics 1694, Springer Verlag, Berlin (1998).
9. m). J. Math. Pure Appl. 75, (1996) 595-626.
10. BRAIDES. A. & DEFRANCESCHI, A. Homogenization of Multiple Integrals. Oxford University Press, Oxford (1998).
11. BRAIDES, A., DAL MASO, G., & GARRONI, A. Variational formulation of softening phenomena in fracture mechanics: the one-dimensional case. Arch. Rational Mech. Anal., to appear.
12. CORTESANI, G. & TOADER, R. A density result in SBV with respect to non-isotropic energies. Nonlinear Analysis, to appear.
13. DAL MASO. G. An Introduction to r-convergence. Birkhäuser, Boston (1993).
14. DE GLORGI, E. Free discontinuity problems in calculus of variations. in DAUTRAY, R. (ed,), Frontiers in Pure and Applied Mathematics, a Collection of Papers Dedicated to J. L. Lions on the Occasion of his 60th Birthday. North Holland (1991).
15. DE GLORGI, E. & AMBROSIO, L. Un nuovo funzionale del calcólo delle variazioni. Atti Accad. Naz. Lincei Rend. Cl. Sei. Fis. Mat. Natur. 82, (1988) 199-210.
16. EVANS, L. C. & GARIEPY, R. F. Measure Theory and Fine Properties of Functions. CRC Press, Boca Raton (1992).
17. FEDERER. H. Geometric Measure Theory. Springer Verlag, New York (1969).
18. LLEBOWITZ. H. Fracture: an Advanced Treatise. Academic Press, San Diego (1969).
19. MODICA, L. & MORTOLA, S. Un esempio di r-convergenza. Boll. Un. Mat. It. 14-B, (1977) 285-299.
20. MUMFORD. D. & SHAH, J. Optimal approximation by piecewise smooth functions and associated variational problems. Comm. Pure Appl. Math. 17, (1989) 577-685.
21. SHAH, J. A common framework for curve evolution, segmentation and anisotropic diffusion. IEEE Conference on Computer Vision and Pattern Recognition, June (1996).
22. SHAH, J. Minimax entropy and learning by diffusion. IEEE Conference on Computer Vision and Pattern Recognition, June (1998).