Concentration and flatness properties of the singular set of bisected balls
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 30 (2001) no. 3-4, pp. 623-659. 
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     title = {Concentration and flatness properties of the singular set of bisected balls},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {623--659},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 30},
     number = {3-4},
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     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2001_4_30_3-4_623_0/}
}
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Maddalena, Francesco; Solimini, Sergio. Concentration and flatness properties of the singular set of bisected balls. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 30 (2001) no. 3-4, pp. 623-659. http://www.numdam.org/item/ASNSP_2001_4_30_3-4_623_0/

[1] R.A. Adams, "Sobolev Spaces", Academic Press, New York, 1975. | MR | Zbl

[2] L. Ambrosio, Compactness theorem for a special class of functions of bounded variation, Boll. Un. Mat. Ital. 3-B (1989), 857-881. | MR | Zbl

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

[4] L. Ambrosio, A new proof of the SBV compactness theorem, Calc. Var. Partial Differential Equations 3 (1995), 127-137. | MR | Zbl

[5] L. Ambrosio - N. Fusco - D. Pallara, Partial Regularity of Free Discontinuity Sets, II, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 24 (1997), 39-62. | Numdam | MR | Zbl

[6] L. Ambrosio - N. Fusco - D. Pallara, "Functions of Bounded Variation and Free Discontinuity Problems", Clarendon Press, Oxford, 2000. | MR | Zbl

[7] Yu. D. Burago - V.A. Zalgaller, "Geometric Inequalities", Springer-Verlag, Berlin, 1988. | MR | Zbl

[8] G. Dal Maso - J.M. Morel - S. Solimini, Une approche variationelle en traitement d'images: résultats d'existence et d'approximation, C. Rend. Acad. Sc. Paris, Série 1, 308 (1989), 549-554. | MR | Zbl

[9] G. Dal Maso - J.M. Morel - S. Solimini, A variational method in image segmentation: existence and approximation results, Acta Math. 168 (1992), 89-15 1. | MR | Zbl

[10] G. David - S. Semmes, On the singular set of minimizers of Mumford-Shah functional, J. Math. Pures Appl.(9) 803 (1989), 549-554.

[11] G. David - S. Semmes, Uniform rectifiability and singular set, Ann. Inst. H. Poincaré Anal. Non Linéaire 13 n. 4 (1996), 383-443. | Numdam | MR | Zbl

[12] E. De Giorgi - L. Ambrosio, Un nuovo tipo di funzionale del calcolo delle variazioni, Atti Acad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei s. 8 82 (1988), 199-210. | MR | Zbl

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

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

[15] E. Giusti, "Minimal Surfaces and Functions of Bounded Variation", Birkhäuser, Boston, 1984. | MR | Zbl

[16] F. Maddalena - S. Solimini, Lower semicontinuity properties for functionals with free discontinuities, Arch. Rational Mech. Anal., to appear. | MR | Zbl

[ 17] F. Maddalena - S. Solimini, Regularity properties offree discontinuity sets, Ann. Inst. H. Poincaré Anal. Non Linéaire, to appear. | Numdam | MR | Zbl

[18] J.M. Morel - S. Solimini, "Variational Methods in Image Segmentation", Birkhäuser, Boston, 1994. | MR

[19] C.B. Morrey, " Variational Multiple Integrals in the Calculus of Variations", Springer Verlag, Heidelberg, New York 1966. | MR | Zbl

[20] D. Mumford - S. Shah, Optimal Approximation by Piecewise Smooth Functions and Associated Variational Problems, Comm. Pure Appl. Math. XLII-4 (1989). | MR | Zbl

[21] R. Rigot, Big pieces of C1,α-graphs for minimizers of the the Mumford-Shah functional, Ann. Scoula Norm. Sup. Pisa Cl. Sci (4) (2000), 329-349. | Numdam | Zbl

[22] S. Solimini, Simplified excision techniques for Free Discontinuity Problems in several variables, J. Funct. Anal. 151 (1997), 1-34. | MR | Zbl