@article{ASNSP_1998_4_27_1_145_0,
author = {Gobbino, Massimo},
title = {Gradient flow for the one-dimensional Mumford-Shah functional},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
publisher = {Scuola normale superiore},
volume = {Ser. 4, 27},
number = {1},
year = {1998},
pages = {145-193},
zbl = {0931.49010},
mrnumber = {1658873},
language = {en},
url = {http://www.numdam.org/item/ASNSP_1998_4_27_1_145_0}
}
Gobbino, Massimo. Gradient flow for the one-dimensional Mumford-Shah functional. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 27 (1998) no. 1, pp. 145-193. http://www.numdam.org/item/ASNSP_1998_4_27_1_145_0/
[ 1 ] , A Compactness Theorem for a New Class of Functions of Bounded Variation, Boll. Un. Mat. Ital. 3-B (1989), 857-881. | MR 1032614 | Zbl 0767.49001
[2] , Existence Theory for a New Class of Variational Problems, Arch. Rational Mech. Anal. 111 (1990), 291-322. | MR 1068374 | Zbl 0711.49064
[3] , Free Discontinuity Problems and Special Functions with Bounded Variation, Proceedings ECM2 Budapest 1996, Progress in Mathematics 168 (1998), 15-35. | MR 1645795 | Zbl 0909.49002
[4] - , Energies in SB V and Variational Models in Fracture Mechanics, in Homogenization and Applications to Material Sciences, (D. Cioranescu, A. Damlamian, P. Donato eds.), Gakuto, Gakkotosho, Tokio, Japan, 1997, p. 1-22. | MR 1473974 | Zbl 0904.73045
[5] - , Approximation of Functionals Depending on Jumps by Elliptic Functionals via r-Convergence, Comm. Pure Appl. Math. 43 (1990), 999-1036. | MR 1075076 | Zbl 0722.49020
[6] , On the Approximation of Free Discontinuity Problems, Boll. Un. Mat. Ital. 6-B (1992), 105-123. | MR 1164940 | Zbl 0776.49029
[7] - , Nonlocal Approximation of the Mumford-Shah Functional, Calc. Var. Partial Differential Equations 5 (1997), 293-322. | MR 1450713 | Zbl 0873.49009
[8] , "Opérateures Maximaux Monotones et Semigroups de Contraction dans les Espaces de Hilbert", North-Holland Mathematics Studies, n. 5 (1973). | MR 348562 | Zbl 0252.47055
[9] , Analyse Fonctionnelle: Theorie et Applications, Masson, 1987. | MR 697382 | Zbl 0511.46001
[10] , Image segmentation by variational methods: Mumford and Shah functional and the discrete approximations, SIAM J. Appl. Math. 55 (1995), 827-863. | MR 1331589 | Zbl 0830.49015
[11] - , Discrete Approximation of the Mumford-Shah Functional in Dimension two, RAIRO Modèl. Math. Anal. Numèr., to appear | Numdam | MR 1726478 | Zbl 0943.49011
[12] - , Minimizing Movements of the Mumford and Shah Energy, Discrete and Continuous Dynamical Systems, vol. 3, n. 2 (1997), 153-174. | MR 1432071 | Zbl 0948.35073
[13] , "An Introduction to Γ-convergence", Birkhäuser, Boston, 1993. | Zbl 0816.49001
[14] - - , Existence theorem for a minimum problem with free discontinuity set, Arch. Rational Mech. Anal. 108 (1989), 195-218. | MR 1012174 | Zbl 0682.49002
[15] - , Su un tipo di convergenza variazionale, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 58 (1975), 842-850. | MR 448194 | Zbl 0339.49005
[16] - - , Problemi di evoluzione in spazi metrici e curve di massima pendenza, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 73 (1982), 6-14. | MR 726279 | Zbl 0521.49011
[17] - , "Measure Theory and Fine Properties of Functions", CRC Press, Boca Raton, 1992. | MR 1158660 | Zbl 0804.28001
[18] , Finite Difference Approximation of the Mumford-Shah Functional, Comm. Pure Appl. Math. 51 (1998), 197-228. | MR 1488299 | Zbl 0888.49013
[19] , The phenomenon of rupture and flow in solids, Phil. Trans. Royal Soc. London Ser. A 221 (1920), 163-198.
[20] , Convergence of the Allen-Cahn Equation to Brakke's Motion by Mean Curvature, J. Differential Geom. 38 (1993), 417-461. | MR 1237490 | Zbl 0784.53035
[21] - , Optimal Approximation by Piecewise Smooth Functions and Associated Variational Problem, Comm. Pure Appl. Math. 17 (1989), 577-685. | MR 997568 | Zbl 0691.49036
[22] , "Weakly Differentiable Functions", Springer, Berlin, 1989. | MR 1014685 | Zbl 0692.46022
