Non-local approximation of free-discontinuity problems with linear growth

 Access to full text

 Full (PDF)

 Access to full text

 Full (PDF)

1. R. Alicandro, A. Braides and M.S. Gelli, Free-discontinuity problems generated by singular perturbation. Proc. Roy. Soc. Edinburgh Sect. A6 (1998) 1115–1129.  
2. R. Alicandro, A. Braides and J. Shah, Free-discontinuity problems via functionals involving the L1-norm of the gradient and their approximations. Interfaces and free boundaries1 (1999) 17–37.  
3. R. Alicandro and M.S. Gelli, Free discontinuity problems generated by singular perturbation: the n-dimensional case. Proc. Roy. Soc. Edinburgh Sect. A130 (2000) 449–469.  
4. L. Ambrosio, A compactness theorem for a new class of functions of bounded variation. Boll. Un. Mat. Ital. B3 (1989) 857–881.  
5. L. Ambrosio, N. Fusco and D. Pallara, Functions of Bounded Variation and Free Discontinuity Problems. Oxford University Press (2000).  
6. L. Ambrosio and V.M. Tortorelli, Approximation of functionals depending on jumps by elliptic functionals via $\Gamma$-convergence. Comm. Pure Appl. Math.XLIII (1990) 999–1036.  
7. L. Ambrosio and V.M. Tortorelli, On the approximation of free discontinuity problems. Boll. Un. Mat. Ital. B (7)VI (1992) 105–123.  
8. G. Bouchitté, A. Braides and G. Buttazzo, Relaxation results for some free discontinuity problems. J. Reine Angew. Math.458 (1995) 1–18.  
9. B. Bourdin and A. Chambolle, Implementation of an adaptive finite-element approximation of the Mumford-Shah functional. Numer. Math.85 (2000) 609–646.  
10. A. Braides. Approximation of free-discontinuity problems. Lect. Notes Math.1694, Springer Verlag, Berlin (1998).  
11. A. Braides and A. Garroni, On the non-local approximation of free-discontinuity problems. Comm. Partial Differential Equations23 (1998) 817–829.  
12. A. Braides and G. Dal Maso, Non-local approximation of the Mumford-Shah functional. Calc. Var.5 (1997) 293–322.  
13. A. Chambolle and G. Dal Maso, Discrete approximation of the Mumford-Shah functional in dimension two. ESAIM: M2AN33 (1999) 651–672.  
14. G. Cortesani, Sequence of non-local functionals which approximate free-discontinuity problems. Arch. Rational Mech. Anal.144 (1998) 357–402.  
15. G. Cortesani, A finite element approximation of an image segmentation problem. Math. Models Methods Appl. Sci.9 (1999) 243–259.  
16. G. Cortesani and R. Toader, Finite element approximation of non-isotropic free-discontinuity problems. Numer. Funct. Anal. Optim.18 (1997) 921–940.  
17. G. Cortesani and R. Toader, A density result in SBV with respect to non-isotropic energies. Nonlinear Anal.38 (1999) 585–604.  
18. G. Cortesani and R. Toader, Nonlocal approximation of nonisotropic free-discontinuity problems. SIAM J. Appl. Math.59 (1999) 1507–1519.  
19. G. Dal Maso, An Introduction to$\Gamma$-Convergence. Birkhäuser, Boston (1993).  
20. E. De Giorgi. Free discontinuity problems in calculus of variations, in Frontiers in pure and applied mathematics. A collection of papers dedicated to Jacques-Louis Lions on the occasion of his sixtieth birthday. June 6–10, Paris 1988, Robert Dautray, Ed., Amsterdam, North-Holland Publishing Co. (1991) 55–62.  
21. L. Lussardi and E. Vitali, Non-local approximation of free-discontinuity functionals with linear growth: the one-dimensional case. Ann. Mat. Pura Appl. (to appear).  
22. M. Morini, Sequences of singularly perturbed functionals generating free-discontinuity problems. SIAM J. Math. Anal.35 (2003) 759–805.  
23. M. Negri, The anisotropy introduced by the mesh in the finite element approximation of the Mumford-Shah functional. Numer. Funct. Anal. Optim.20 (1999) 957–982.  
24. S. Osher and J.A. Sethian, Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations. J. Comput. Phys.79 (1988) 12–49.  
25. J. Shah, A common framework for curve evolution, segmentation and anisotropic diffusion, in IEEE conference on computer vision and pattern recognition (1996).  
26. J. Shah, Uses of elliptic approximations in computer vision. In R. Serapioni and F. Tomarelli, editors, Progress in Nonlinear Differential Equations and Their Applications25 (1996).  
27. L. Simon, Lectures on Geometric Measure Theory. Centre for Mathematical Analysis, Australian National University (1984).  

1. Luca Lussardi, Risultati di approssimazione per funzionali a discontinuità libera a crescita lineare
2. Luca Lussardi, Annibale Magni, Γ-limits of convolution functionals