Big pieces of C 1,α -graphs for minimizers of the Mumford-Shah functional
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 29 (2000) no. 2, pp. 329-349.
@article{ASNSP_2000_4_29_2_329_0,
     author = {Rigot, S\'everine},
     title = {Big pieces of $C^{1, \alpha }$-graphs for minimizers of the {Mumford-Shah} functional},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {329--349},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 29},
     number = {2},
     year = {2000},
     zbl = {0960.49024},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2000_4_29_2_329_0/}
}
TY  - JOUR
AU  - Rigot, Séverine
TI  - Big pieces of $C^{1, \alpha }$-graphs for minimizers of the Mumford-Shah functional
JO  - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY  - 2000
SP  - 329
EP  - 349
VL  - 29
IS  - 2
PB  - Scuola normale superiore
UR  - http://www.numdam.org/item/ASNSP_2000_4_29_2_329_0/
LA  - en
ID  - ASNSP_2000_4_29_2_329_0
ER  - 
%0 Journal Article
%A Rigot, Séverine
%T Big pieces of $C^{1, \alpha }$-graphs for minimizers of the Mumford-Shah functional
%J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
%D 2000
%P 329-349
%V 29
%N 2
%I Scuola normale superiore
%U http://www.numdam.org/item/ASNSP_2000_4_29_2_329_0/
%G en
%F ASNSP_2000_4_29_2_329_0
Rigot, Séverine. Big pieces of $C^{1, \alpha }$-graphs for minimizers of the Mumford-Shah functional. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 29 (2000) no. 2, pp. 329-349. http://www.numdam.org/item/ASNSP_2000_4_29_2_329_0/

[1] 'R. Adams, "Sobolev Spaces", Academic Press, New York-London, 1975. | 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 - 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

[4] M. Carriero - A. Leaci, Existence theorem for a Dirichlet problem with free discontinuity set, Nonlinear Anal. 15 (1990), 661-677. | MR | Zbl

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

[6] G. David, "Wavelets and singular integrals on curves and surfaces", Lecture Notes in Math, Vol. 1465, Springer-Verlag, Berlin, 1991. | MR | Zbl

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

[8] G. David - S. Semmes, "Analysis of and on uniformly rectifiable sets", Math. Surveys Monogr., Vol. 38, Amer. Math. Soc., Providence, 1993. | MR | Zbl

[9] G. David - S. Semmes, On the singular sets of minimizers of the Mumford-Shahfunctional, J. Math. Pures Appl. (4) 75 (1996), 299-342. | MR | Zbl

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

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

[12] F. Maddalena - S. Solimini, Regularity properties of free discontinuity sets, preprint.

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