Cracktip is a global Mumford-Shah minimizer
Astérisque, no. 274 (2001) , 265 p.
@book{AST_2001__274__R1_0,
     author = {Bonnet, Alexis and David, Guy},
     title = {Cracktip is a global {Mumford-Shah} minimizer},
     series = {Ast\'erisque},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {274},
     year = {2001},
     mrnumber = {1864620},
     zbl = {1014.49009},
     language = {en},
     url = {http://www.numdam.org/item/AST_2001__274__R1_0/}
}
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%A David, Guy
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Bonnet, Alexis; David, Guy. Cracktip is a global Mumford-Shah minimizer. Astérisque, no. 274 (2001), 265 p. http://numdam.org/item/AST_2001__274__R1_0/

[Am] L. Ambrosio, Existence theory for a new class of variational problems, Arch. Rational Mech. Anal. 111 (1990), 291-322. | MR | Zbl | DOI

[AmPa] L. Ambrosio and D. Pallara. Partial regularity of free discontinuity sets I., Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 24 (1997), 1-38. | MR | Zbl | EuDML | Numdam

[AFP] L. Ambrosio, N. Fusco and D. Pallara, Partial regularity of free discontinuity sets II, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 24 (1997), 39-62. | MR | Zbl | EuDML | Numdam

[AFP2] L. Ambrosio, N. Fusco and D. Pallara, Higher regularity of solutions of free discontinuity problems. Differential Integral Equations 12 (1999), no. 4, 499-520. | MR | Zbl

[Bo] A. Bonnet, On the regularity of edges in image segmentation, Ann. Inst. H. Poincaré, Analyse non linéaire, vol. 13, 4 (1996), 485-528. | MR | Zbl | EuDML | Numdam | DOI

[DMS] G. Dal Maso, J.-M. Morel, and S. Solimini, A variational method in image segmentation: Existence and approximation results, Acta Math. 168 (1992), 89-151. | MR | Zbl | DOI

[Da] G. David, C-1 arcs for minimizers of the Mumford-Shah functional, SIAM. Journal of Appi. Math., vol. 56, no. 3 (1996), 783-888. | MR | Zbl

[DaLé] G. David and J.-C. Léger, Monotonicity and separation for the Mumford- Shah problem, manuscript. | Zbl | Numdam | DOI

[DaSel] G. David and S. Semmes, Analysis of and on uniformly rectifiable sets, A.M.S series of Mathematical surveys and monographs, vol. 38, 1993. | MR | Zbl | DOI

[DaSe2] G. David and S. Semmes, On the singular sets of minimizers of the Mumford-Shah functional, Journal de Math. Pures et Appl. 75 (1996), 299-342. | MR | Zbl

[DaSe3] G. David and S. Semmes, On a variational problem from image processing, proceedings of the conference in honor of J.-P. Kahane, special issue of the Journal of Fourier Analysis and Applications, 1995, 161-187. | MR | Zbl

[DG] E. De Giorgi, Problemi con discontinuità libera, Int. Symp. Renato Caccioppoli, Napoli, Sept. 20-22, 1989. Ricerche Mat. 40 (1991), suppl. 203-214. | Zbl

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

[Di] F. Dibos, Uniform rectifiability of image segmentations obtained by a variational method, Journal de Math. Pures et Appl. 73, 1994, 389-412. | MR | Zbl

[DiKo] F. Dibos and G. Koepfler, Propriété de régularité des contours d'une image segmentée, Comptes Rendus Acad. Sc. Paris 313 (1991), 573-578. | MR | Zbl

[DiSe] F. Dibos and E. Séré, An approximation result for Minimizers of the Mumford-Shah functional, Boll. Un. Mat. Ital. A(7), 11 (1997), 149-162. | MR | Zbl

[Fa] K. Falconer, The Geometry of fractal sets, Cambridge University Press 1984. | Zbl | MR

[Fe] H. Federer, Geometric measure theory, Grundlehren der Mathematishen Wissenschaften 153, Springer Verlag 1969. | MR | Zbl

[HaKo] P. Hajlasz, and P. Koskela, Sobolev met Poincaré, Mem. Amer. Math. Soc. 145 (2000), no. 688. | MR | Zbl

[HaLiPo] G. Hardy, J. E. Littlewood, and G. Pólya, Inequalities, Second Edition, Cambridge University Press 1952. | MR | Zbl

[Ga] J. Garnett, Bounded analytic functions, Pure and Applied Mathematics 96, Academic Press 1981. | MR | Zbl

[Lé1] J.-C. Léger, Une remarque sur la régularité d'une image segmentée, Journal de Math, pures et appliquées 73, 1994, 567-577. | MR | Zbl

[Lé2] J.-C. Léger, Flatness and finiteness in the Mumford-Shah problem, J. Math. Pures Appl. (9) 78 (1999), no. 4, 431-459. | MR | Zbl | DOI

[Lé3] J.-C. Léger, Courbure de Menger et rectifiabilité et Sur la fonctionnelle de Mumford-Shah, thèse, Paris-Sud Orsay, January 1997.

[MaSo] F. Maddalena and S. Solimini, Lower semicontinuity properties for functionals with free discontinuities, to exist. | Zbl | DOI

[Ma] P. Mattila, Geometry of sets and measures in Euclidean space, Cambridge Studies in Advanced Mathematics 44, Cambridge University Press 1995. | MR | Zbl

[MoSo] J.-M. Morel and S. Solimini, Variational methods in image segmentation, Progress in nonlinear differential equations and their applications 14, Birkhauser 1995. | MR

[MuSh] D. Mumford and J. Shah, Optimal approximations by piecewise smooth functions and associated variational problems. Comm. Pure Appl. Math. 42 (1989), 577-685. | MR | Zbl | DOI

[Po] C. Pommerenke, Boundary behavior of conformal maps, Grundslehren der Mathematischen Wissenchaften 299, Springer-Verlag 1992. | MR | Zbl | DOI

[St] E. M. Stein, Singular integrals and differentiability properties of functions, Princenton university press 1970. | MR | Zbl