Regularity of the singular set for Mumford-Shah minimizers in R^3 near a minimal cone

Details Regularity of the singular set for Mumford-Shah minimizers in R^3 near a minimal cone Regularity of the singular set for Mumford-Shah minimizers in R^3 near a minimal cone

2008-06-18

arxiv.org/abs/0806.2994v1

Mathematics

Analysis of PDEs

46 pages

Scientific paper

We show that if (u;K) is a minimizer of the Mumford-Shah functional in an open set of R^3, 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 C^1,alpha equivalent to the minimal cone in B(x; cr) where c < 1 is an universal constant.

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