Endpoint regularity for $2d$ Mumford-Shah minimizers: On a theorem of Andersson and Mikayelyan

TL;DR

This paper provides an alternative proof of the regularity of 2D Mumford-Shah minimizers near crack tips and single-arc configurations, enhancing understanding of their geometric structure.

Contribution

It offers a new proof of regularity results for Mumford-Shah minimizers in 2D, refining previous theorems by Andersson and Mikayelyan.

Findings

Regularity of minimizers near crack tips established

Single-arc minimizers shown to be regular at interior endpoints

Enhanced understanding of geometric structure of Mumford-Shah minimizers

Abstract

We give an alternative proof of the regularity, up to the loose end, of minimizers, resp. critical points of the Mumford-Shah functional when they are sufficiently close to the cracktip, resp. they consist of a single arc terminating at an interior point.