Un théorème de régularité pour les minimiseurs de Mumford-Shah dans ℝ 3
Séminaire Équations aux dérivées partielles (Polytechnique) (2009-2010), Talk no. 25, 11 p. 
@article{SEDP_2009-2010____A25_0,
     author = {Lemenant, Antoine},
     title = {Un th\'eor\`eme de r\'egularit\'e pour les minimiseurs de Mumford-Shah dans $\mathbb{R}^3$},
     journal = {S\'eminaire \'Equations aux d\'eriv\'ees partielles (Polytechnique)},
     publisher = {Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
     year = {2009-2010},
     note = {talk:25},
     language = {fr},
     url = {http://www.numdam.org/item/SEDP_2009-2010____A25_0}
}

Lemenant, Antoine. Un théorème de régularité pour les minimiseurs de Mumford-Shah dans $\mathbb{R}^3$. Séminaire Équations aux dérivées partielles (Polytechnique) (2009-2010), Talk no. 25, 11 p. http://www.numdam.org/item/SEDP_2009-2010____A25_0/

[1] Luigi Ambrosio, Nicola Fusco, and Diego Pallara. Partial regularity of free discontinuity sets. II. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 24(1) :39–62, 1997. | Numdam | MR 1475772 | Zbl 0896.49024

[2] Luigi Ambrosio, Nicola Fusco, and Diego Pallara. Functions of bounded variation and free discontinuity problems. Oxford Mathematical Monographs. The Clarendon Press Oxford University Press, New York, 2000. | MR 1857292 | Zbl 0957.49001

[3] Luigi Ambrosio and Diego Pallara. Partial regularity of free discontinuity sets. I. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 24(1) :1–38, 1997. | Numdam | MR 1475771 | Zbl 0896.49023

[4] A. Bonnet. On the regularity of edges in image segmentation. Ann. Inst. H. Poincaré Anal. Non Linéaire, 13(4) :485–528, 1996. | Numdam | MR 1404319 | Zbl 0883.49004

[5] Guy David. C 1+α -regularity for two dimensional almost-minimal sets in ℝ n . (2008) Preprint Available at http://www.math.u-psud.fr/~gdavid/. | MR 2683770

[6] Guy David. C 1 -arcs for minimizers of the Mumford-Shah functional. SIAM J. Appl. Math., 56(3) :783–888, 1996. | MR 1389754 | Zbl 0870.49020

[7] Guy David. Singular sets of minimizers for the Mumford-Shah functional, volume 233 of Progress in Mathematics. Birkhäuser Verlag, Basel, 2005. | MR 2129693 | Zbl 1086.49030

[8] Guy David. Hölder regularity of two-dimensional almost-minimal sets in ℝ n . Ann. Fac. Sci. Toulouse Math. (6), 18(1) :65–246, 2009. | Numdam | MR 2518104 | Zbl 1213.49051

[9] Guy David, Thierry De Pauw, and Tatiana Toro. A generalization of Reifenberg’s theorem in ℝ 3 . Geom. Funct. Anal., 18(4) :1168–1235, 2008. | MR 2465688 | Zbl 1169.49040

[10] E. De Giorgi, M. Carriero, and A. Leaci. Existence theorem for a minimum problem with free discontinuity set. Arch. Rational Mech. Anal., 108(3) :195–218, 1989. | MR 1012174 | Zbl 0682.49002

[11] Herbert Koch, Giovanni Leoni, and Massimiliano Morini. On optimal regularity of free boundary problems and a conjecture of De Giorgi. Comm. Pure Appl. Math., 58(8) :1051–1076, 2005. | MR 2143526 | Zbl 1082.35168

[12] Antoine Lemenant. Regularity of the singular set for Mumford-Shah minimizers in ℝ 3 near a minimal cone. To apear in Ann. Scu. Norm. Sup. Pisa. | Zbl 1239.49062

[13] Antoine Lemenant. Sur la régularité des minimiseurs de Mumford-Shah en dimension 3 et supérieure. Thesis Université Paris Sud XI, Orsay, 2008.

[14] Antoine Lemenant. Energy improvement for energy minimizing functions in the complement of generalized Reifenberg-flat sets. Ann. Scuola Norm. Sup. Pisa Cl. Sci., IX(5) :1–34, 2010. | Numdam | MR 2731160 | Zbl 1197.49050

[15] David Mumford and Jayant Shah. Optimal approximations by piecewise smooth functions and associated variational problems. Comm. Pure Appl. Math., 42(5) :577–685, 1989. | MR 997568 | Zbl 0691.49036

[16] Jean E. Taylor. The structure of singularities in soap-bubble-like and soap-film-like minimal surfaces. Ann. of Math. (2), 103(3) :489–539, 1976. | MR 428181 | Zbl 0335.49032