Gradient flow for the one-dimensional Mumford-Shah functional
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 27 (1998) no. 1, pp. 145-193.
@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},
     pages = {145--193},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 27},
     number = {1},
     year = {1998},
     mrnumber = {1658873},
     zbl = {0931.49010},
     language = {en},
     url = {http://archive.numdam.org/item/ASNSP_1998_4_27_1_145_0/}
}
TY  - JOUR
AU  - Gobbino, Massimo
TI  - Gradient flow for the one-dimensional Mumford-Shah functional
JO  - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY  - 1998
SP  - 145
EP  - 193
VL  - 27
IS  - 1
PB  - Scuola normale superiore
UR  - http://archive.numdam.org/item/ASNSP_1998_4_27_1_145_0/
LA  - en
ID  - ASNSP_1998_4_27_1_145_0
ER  - 
%0 Journal Article
%A Gobbino, Massimo
%T Gradient flow for the one-dimensional Mumford-Shah functional
%J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
%D 1998
%P 145-193
%V 27
%N 1
%I Scuola normale superiore
%U http://archive.numdam.org/item/ASNSP_1998_4_27_1_145_0/
%G en
%F 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, Serie 4, Volume 27 (1998) no. 1, pp. 145-193. http://archive.numdam.org/item/ASNSP_1998_4_27_1_145_0/

[ 1 ] L. Ambrosio, A Compactness Theorem for a New Class of Functions of Bounded Variation, Boll. Un. Mat. Ital. 3-B (1989), 857-881. | MR | Zbl

[2] L. Ambrosio, Existence Theory for a New Class of Variational Problems, Arch. Rational Mech. Anal. 111 (1990), 291-322. | MR | Zbl

[3] L. Ambrosio, Free Discontinuity Problems and Special Functions with Bounded Variation, Proceedings ECM2 Budapest 1996, Progress in Mathematics 168 (1998), 15-35. | MR | Zbl

[4] L. Ambrosio - A. Braides, 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 | Zbl

[5] L. Ambrosio - V.M. Tortorelli, Approximation of Functionals Depending on Jumps by Elliptic Functionals via r-Convergence, Comm. Pure Appl. Math. 43 (1990), 999-1036. | MR | Zbl

[6] L. Ambrosio-. M. Tortorelli, On the Approximation of Free Discontinuity Problems, Boll. Un. Mat. Ital. 6-B (1992), 105-123. | MR | Zbl

[7] A. Braides - G. Dal Maso, Nonlocal Approximation of the Mumford-Shah Functional, Calc. Var. Partial Differential Equations 5 (1997), 293-322. | MR | Zbl

[8] H. Brezis, "Opérateures Maximaux Monotones et Semigroups de Contraction dans les Espaces de Hilbert", North-Holland Mathematics Studies, n. 5 (1973). | MR | Zbl

[9] H. Brezis, Analyse Fonctionnelle: Theorie et Applications, Masson, 1987. | MR | Zbl

[10] A. Chambolle, Image segmentation by variational methods: Mumford and Shah functional and the discrete approximations, SIAM J. Appl. Math. 55 (1995), 827-863. | MR | Zbl

[11] A. Chambolle - G. Dal Maso, Discrete Approximation of the Mumford-Shah Functional in Dimension two, RAIRO Modèl. Math. Anal. Numèr., to appear | Numdam | MR | Zbl

[12] A. Chambolle - F. Doveri, Minimizing Movements of the Mumford and Shah Energy, Discrete and Continuous Dynamical Systems, vol. 3, n. 2 (1997), 153-174. | MR | Zbl

[13] G. Dal Maso, "An Introduction to Γ-convergence", Birkhäuser, Boston, 1993. | Zbl

[14] E. De Giorgi - G. Carriero - A. Leaci, Existence theorem for a minimum problem with free discontinuity set, Arch. Rational Mech. Anal. 108 (1989), 195-218. | MR | Zbl

[15] E. De Giorgi - T. Franzoni, Su un tipo di convergenza variazionale, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 58 (1975), 842-850. | MR | Zbl

[16] E. De Giorgi - A. Marino - M. Tosques, 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 | Zbl

[17] L.C. Evans - R.F. Gariepy, "Measure Theory and Fine Properties of Functions", CRC Press, Boca Raton, 1992. | MR | Zbl

[18] M. Gobbino, Finite Difference Approximation of the Mumford-Shah Functional, Comm. Pure Appl. Math. 51 (1998), 197-228. | MR | Zbl

[19] A.A. Griffiths, The phenomenon of rupture and flow in solids, Phil. Trans. Royal Soc. London Ser. A 221 (1920), 163-198.

[20] T. Ilmanen, Convergence of the Allen-Cahn Equation to Brakke's Motion by Mean Curvature, J. Differential Geom. 38 (1993), 417-461. | MR | Zbl

[21] D. Mumford - J. Shah, Optimal Approximation by Piecewise Smooth Functions and Associated Variational Problem, Comm. Pure Appl. Math. 17 (1989), 577-685. | MR | Zbl

[22] W.P. Ziemer, "Weakly Differentiable Functions", Springer, Berlin, 1989. | MR | Zbl