Regularity properties of free discontinuity sets
Annales de l'I.H.P. Analyse non linéaire, Tome 18 (2001) no. 6, pp. 675-685. 
@article{AIHPC_2001__18_6_675_0,
     author = {Maddalena, Francesco and Solimini, Sergio},
     title = {Regularity properties of free discontinuity sets},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {675--685},
     publisher = {Elsevier},
     volume = {18},
     number = {6},
     year = {2001},
     mrnumber = {1860951},
     zbl = {1024.49013},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2001__18_6_675_0/}
}
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Maddalena, Francesco; Solimini, Sergio. Regularity properties of free discontinuity sets. Annales de l'I.H.P. Analyse non linéaire, Tome 18 (2001) no. 6, pp. 675-685. http://www.numdam.org/item/AIHPC_2001__18_6_675_0/

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

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

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

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

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

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

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

[8] David G., C1 arcs for the minimizers of the Mumford-Shah functional, SIAM J. Appl. Math. 56 (1996) 783-888. | MR | Zbl

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

[10] David G., Semmes S., Fractured Fractals and Broken Dreams, Clarendon Press, Oxford, 1997. | MR | Zbl

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

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

[13] Maddalena F., Solimini S., Concentration and flatness properties of bisected balls, Ann. Scuola Norm. Sup. Pisa (to appear).

[14] Maddalena F., Solimini S., Lower semicontinuity properties for functionals with free discontinuities, Arch. Rat. Mech. Anal. (to appear). | MR | Zbl

[15] Maddalena F., Solimini S., Blow-up techniques and regularity near the boundary for free discontinuity problems, in preparation. | Zbl

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

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

[18] Mumford D., Shah S., Optimal approximation by piecewise smooth functions and associated variational problems, Comma. Pure Apple. Math. LXII-4 (1989). | Zbl

[19] Rigot S., 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

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