Regularity of the singular set for Mumford-Shah minimizers in R³ near a minimal cone

2008/06/18 by Lemenant, Antoine · 1 citation
#49Q20 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.0806.2994

Abstract

We show that if (u;K) is a minimizer of the Mumford-Shah functional in an open set of R³, and if x, K and r > 0 are such that K is close enough to a minimal cone of type P (a plane), Y (three half planes meeting with 120 degrees angles) or T (cone over a regular tetrahedron centered at the origin) in terms of Hausdorff distance in B(x; r), then K is C¹,alpha equivalent to the minimal cone in B(x; cr) where c < 1 is an universal constant.

Cited by

• Hausdorff dimension of the singular set for Griffith almost-minimizers in the plane

Related

• A rigidity result for global Mumford-Shah minimizers in dimension three
• Numerical study of a new global minimizer for the Mumford-Shah functional in \R³
• On the homogeneity of global minimizers for the Mumford-Shah functional when K is a smooth cone
• The regularity theory for the Mumford-Shah functional on the plane
• Fine regularity results for Mumford-Shah minimizers: porosity, higher integrability and the Mumford-Shah conjecture