Rigot, Séverine
Big pieces of C 1,α -graphs for minimizers of the Mumford-Shah functional
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4 : Tome 29 (2000) no. 2 , p. 329-349
Zbl 0960.49024 | 3 citations dans Numdam
URL stable : http://www.numdam.org/item?id=ASNSP_2000_4_29_2_329_0

Bibliographie

[1] 'R. Adams, "Sobolev Spaces", Academic Press, New York-London, 1975. MR 450957 | Zbl 0314.46030

[2] L. Ambrosio, Existence theory for a new class of variational problems, Arch. Rational Mech. Anal. 111 (1990), 291-322. MR 1068374 | Zbl 0711.49064

[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 1475772 | Zbl 0896.49024

[4] M. Carriero - A. Leaci, Existence theorem for a Dirichlet problem with free discontinuity set, Nonlinear Anal. 15 (1990), 661-677. MR 1073957 | Zbl 0713.49003

[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 1149865 | Zbl 0772.49006

[6] G. David, "Wavelets and singular integrals on curves and surfaces", Lecture Notes in Math, Vol. 1465, Springer-Verlag, Berlin, 1991. MR 1123480 | Zbl 0764.42019

[7] G. David, C1-arcs for minimizers of the Mumford-Shah functional,, SIAM J. Appl. Math 56 (1996), 783-888. MR 1389754 | Zbl 0870.49020

[8] G. David - S. Semmes, "Analysis of and on uniformly rectifiable sets", Math. Surveys Monogr., Vol. 38, Amer. Math. Soc., Providence, 1993. MR 1251061 | Zbl 0832.42008

[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 1411155 | Zbl 0853.49010

[10] G. David - S. Semmes, Uniform rectifiability and singular sets, Ann. Inst. H. Poincaré Anal. Non Linéaire 13 (1996), 383-443. | Numdam | MR 1404317 | Zbl 0908.49030

[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 1012174 | Zbl 0682.49002

[12] F. Maddalena - S. Solimini, Regularity properties of free discontinuity sets, preprint. Zbl 1024.49013

[13] D. Mumford - J. Shah, Optimal approximations by piecewise smooth functions and associated variational problems, Comm. Pure Appl. Math. 42 (1989), 577-685. MR 997568 | Zbl 0691.49036