On the existence of solutions to a problem in multidimensional segmentation
Congedo, G. ; Tamanini, I.
Annales de l'I.H.P. Analyse non linéaire, Tome 8 (1991), p. 175-195 / Harvested from Numdam
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@article{AIHPC_1991__8_2_175_0,
     author = {Congedo, Giuseppe and Tamanini, I.},
     title = {On the existence of solutions to a problem in multidimensional segmentation},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {8},
     year = {1991},
     pages = {175-195},
     mrnumber = {1096603},
     zbl = {0729.49003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_1991__8_2_175_0}
}

Congedo, G.; Tamanini, I. On the existence of solutions to a problem in multidimensional segmentation. Annales de l'I.H.P. Analyse non linéaire, Tome 8 (1991) pp. 175-195. http://gdmltest.u-ga.fr/item/AIHPC_1991__8_2_175_0/

[A1m] F.J. Almgren, Existence and Regularity Almost Everywhere of Solutions to Elliptic Variations Problems with Constraints, Mem. A.M.S., Vol. 4, No. 165, 1976. | MR 420406 | Zbl 0327.49043

[A1] L. Ambrosio, A Compactness Theorem for a Special Class of Functions of Bounded Variation, Boll. Un. Mat. Ital. (to appear).

[A2] L. Ambrosio, Existence Theory for a New Class of Variational Problems, Arch. Rat. Mech. Anal., (to appear). | MR 1068374 | Zbl 0711.49064

[A-B] L. Ambrosio and A. Braides, Functionals defined on partitions... I et II, J. Math. Pures Appl. (to appear).

[B-M] J. Blat and J.M. Morel, Elliptic Problems in Image Segmentation (to appear).

[C-T1] G. Congedo and I. Tamanini, Note sulla regolarità dei minimi di funzionali del tipo dell'area, Rend. Accad. Naz. XL, 106, Vol. XII, fasc. 17, 1988, pp. 239-257. | MR 985069 | Zbl 0674.49031

[C-T2] G. Congedo and I. Tamanini, Density Theorems for Local Minimizers of Area-Type Functionals (to appear). | Numdam | MR 1142542

[DeG] E. De Giorgi, Free Discontinuity Problems in Calculus of Variations, Proceedings of the meeting in J. L. Lions's honour, Paris, 1988 (to appear). | Zbl 0758.49002

[DeG-A] E. De Giorgi and L. Ambrosio, Un nuovo tipo di funzionale del calcolo delle variazioni, Atti Accad. Naz. Lincei (to appear).

[DeG-C-L] E. De Giorgi, M. Carriero and A. Leaci, Existence Theorem for a minimum Problem with Free Discontinuity Set, Arch. Rat. Mech. Anal., Vol. 108, 1989, pp. 195-218. | MR 1012174 | Zbl 0682.49002

[DeG-C-P] E. De Giorgi, F. Colombini and L.C. Piccinini, Frontiere orientate di misura minima e questioni collegate, Editrice Tecnico Scientifica, Pisa, 1972. | Zbl 0296.49031

[DeG-C-T] E. De Giorgi, G. Congedo and I. Tamanini, Problemi di regolarità per un nuovo tipo di funzionale del calcolo delle variazioni, Atti Accad. Naz. Lincei (to appear).

[F] H. Federer, Geometric Measure Theory, Springer-Verlag, Berlin, 1969. | MR 257325 | Zbl 0176.00801

[G] E. Giusti, Minimal Surfaces and Functions of Bounded Variation, Birkhäuser, Boston, 1984. | MR 775682 | Zbl 0545.49018

[M-M] U. Massari and M. Miranda, Minimal Surfaces of Codimension 1, North-Holland, Amsterdam, 1984. | MR 795963 | Zbl 0565.49030

[M-T] U. Massari, I. Tamanini, paper in preparation.

[Mo-S] J.M. Morel and S. Solimini, Segmentation of Images by Variational Methods: a Constructive Approach, Rev. Mat. Univ. Complutense Madrid, Vol. 1, 1988, pp. 169-182. | MR 977048 | Zbl 0679.68205

[M-S] D. Mumford and J. Shah, Optimal Approximations by Piecewise Smooth Functions and Associated Variational Problems, Comm. Pure Appl. Math., Vol. 42, 1989, pp. 577-685. | MR 997568 | Zbl 0691.49036

[S] L. Simon, Lectures on Geometric Measure Theory, Center for Math. Analysis, Australian National University, Vol., 3, 1983. | MR 756417 | Zbl 0546.49019

[T1] J.E. Taylor, The Structure of Singularities in Soap-Bubble-Like and Soap-Film-Like Minimal Surfaces, Annals Math., 103, 1976, pp. 489-539. | MR 428181 | Zbl 0335.49032

[T2] J.E. Taylor, Cristalline Variational Problems, Bull. A.M.S., Vol. 84, 1978, pp. 568-588. | MR 493671 | Zbl 0392.49022