Regularity of the singular set for Mumford-Shah minimizers in 3 near a minimal cone
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 10 (2011) no. 3, p. 561-609

We prove that if (u,K) is a minimizer of the Mumford-Shah functional in an open set Ω of 3 , and if xK and r>0 are such that K is close enough to a minimal cone of type (a plane), 𝕐 (three half planes meeting at x with 120 angles) or 𝕋 (cone over the 6 edges of a regular tetrahedron centered at x) in terms of Hausdorff distance in B(x,r), then K is C 1,α equivalent to the minimal cone in B(x,cr) where c<1 is a universal constant.

Published online : 2018-06-21
Classification:  49Q20,  49Q05
@article{ASNSP_2011_5_10_3_561_0,
     author = {Lemenant, Antoine},
     title = {Regularity of the singular set for Mumford-Shah minimizers in $\protect \mathbb{R}^3$ near a minimal cone},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 10},
     number = {3},
     year = {2011},
     pages = {561-609},
     zbl = {1239.49062},
     mrnumber = {2905379},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2011_5_10_3_561_0}
}
Lemenant, Antoine. Regularity of the singular set for Mumford-Shah minimizers in $\protect \mathbb{R}^3$ near a minimal cone. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 10 (2011) no. 3, pp. 561-609. http://www.numdam.org/item/ASNSP_2011_5_10_3_561_0/

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