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, Série 5, Tome 10 (2011) no. 3, pp. 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.

Publié le :
Classification : 49Q20, 49Q05
Lemenant, Antoine 1

1 Université Denis Diderot - Paris 7 U.F.R de Mathématiques Site Chevaleret Case 7012 175, rue du Chevaleret 75205 Paris Cedex 13 (France) lemenant@ann.jussieu.fr
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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, Série 5, Tome 10 (2011) no. 3, pp. 561-609. http://www.numdam.org/item/ASNSP_2011_5_10_3_561_0/

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