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

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.

27 pages. v3: corrected typos, added proof of (8.1), corrected acknowledgements. To appear in Journal de Mathématiques Pures et Appliquées. For Errata see https://www.math.ias.edu/delellis/sites/math.ias.edu.delellis/files/Errata-crackip.pdf