- R. Alicandro, A. Braides and M.S. Gelli, Free-discontinuity problems generated by singular perturbation. Proc. Roy. Soc. Edinburgh Sect. A 6 (1998) 1115–1129.
- 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 boundaries 1 (1999) 17–37. [CrossRef] [MathSciNet]
- R. Alicandro and M.S. Gelli, Free discontinuity problems generated by singular perturbation: the n-dimensional case. Proc. Roy. Soc. Edinburgh Sect. A 130 (2000) 449–469. [MathSciNet]
- L. Ambrosio, A compactness theorem for a new class of functions of bounded variation. Boll. Un. Mat. Ital. B 3 (1989) 857–881. [MathSciNet]
- L. Ambrosio, N. Fusco and D. Pallara, Functions of Bounded Variation and Free Discontinuity Problems. Oxford University Press (2000).
- L. Ambrosio and V.M. Tortorelli, Approximation of functionals depending on jumps by elliptic functionals via -convergence. Comm. Pure Appl. Math. XLIII (1990) 999–1036.
- L. Ambrosio and V.M. Tortorelli, On the approximation of free discontinuity problems. Boll. Un. Mat. Ital. B (7) VI (1992) 105–123.
- G. Bouchitté, A. Braides and G. Buttazzo, Relaxation results for some free discontinuity problems. J. Reine Angew. Math. 458 (1995) 1–18. [MathSciNet]
- B. Bourdin and A. Chambolle, Implementation of an adaptive finite-element approximation of the Mumford-Shah functional. Numer. Math. 85 (2000) 609–646. [CrossRef] [MathSciNet]
- A. Braides. Approximation of free-discontinuity problems. Lect. Notes Math. 1694, Springer Verlag, Berlin (1998).
- A. Braides and A. Garroni, On the non-local approximation of free-discontinuity problems. Comm. Partial Differential Equations 23 (1998) 817–829. [CrossRef] [MathSciNet]
- A. Braides and G. Dal Maso, Non-local approximation of the Mumford-Shah functional. Calc. Var. 5 (1997) 293–322. [CrossRef] [MathSciNet]
- A. Chambolle and G. Dal Maso, Discrete approximation of the Mumford-Shah functional in dimension two. ESAIM: M2AN 33 (1999) 651–672. [CrossRef] [EDP Sciences]
- G. Cortesani, Sequence of non-local functionals which approximate free-discontinuity problems. Arch. Rational Mech. Anal. 144 (1998) 357–402. [CrossRef] [MathSciNet]
- G. Cortesani, A finite element approximation of an image segmentation problem. Math. Models Methods Appl. Sci. 9 (1999) 243–259. [CrossRef] [MathSciNet]
- G. Cortesani and R. Toader, Finite element approximation of non-isotropic free-discontinuity problems. Numer. Funct. Anal. Optim. 18 (1997) 921–940. [CrossRef] [MathSciNet]
- G. Cortesani and R. Toader, A density result in SBV with respect to non-isotropic energies. Nonlinear Anal. 38 (1999) 585–604. [CrossRef] [MathSciNet]
- G. Cortesani and R. Toader, Nonlocal approximation of nonisotropic free-discontinuity problems. SIAM J. Appl. Math. 59 (1999) 1507–1519. [CrossRef] [MathSciNet]
- G. Dal Maso, An Introduction to -Convergence. Birkhäuser, Boston (1993).
- 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.
- 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).
- M. Morini, Sequences of singularly perturbed functionals generating free-discontinuity problems. SIAM J. Math. Anal. 35 (2003) 759–805. [CrossRef] [MathSciNet]
- 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. [CrossRef] [MathSciNet]
- 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. [NASA ADS] [CrossRef] [MathSciNet]
- J. Shah, A common framework for curve evolution, segmentation and anisotropic diffusion, in IEEE conference on computer vision and pattern recognition (1996).
- J. Shah, Uses of elliptic approximations in computer vision. In R. Serapioni and F. Tomarelli, editors, Progress in Nonlinear Differential Equations and Their Applications 25 (1996).
- L. Simon, Lectures on Geometric Measure Theory. Centre for Mathematical Analysis, Australian National University (1984).
Volume 13, Number 1, January-March 2007
|Page(s)||135 - 162|
|Published online||14 February 2007|