Zu Chongzhi Research Seminar

Date and Time (China standard time): Friday, January 16, 2026, 11:00 am – 12:00 pm

Location: WDR 1007

Zoom: 99203198372, Passcode: dkumath

Title: A missing Euler-Lagrange condition for the Mumford-Shah functional

Speaker: Hayk Mikayelyan, University of Nottingham Ningbo China

Abstract: Some old results about the asymptotics of the Mumford-Shah minimizers near the crack-tip, as well as the curvature will be presented, which leads to new Euler-Lagrange condition.

We also develop a new numerical method to compute the minimizers in 2D, which is very accurate near the crack-tip.

In 3D we construct a continuous family of stationary solutions which are not global minimizers. We make a conjecture that the dependence of the function on the point running over the crack-front is related to the behavior of the co-normal tangent at the crack-front. (joint work with John Andersson, Antoine Lemenant and Zhilin Li)

Bio: Dr Hayk Mikayelyan has graduated from Yerevan State University in Armenia (1999) and obtained his PhD from Potsdam University in Germany (2003). After a PostDoc position at Leipzig University he joined the Max Planck Institute for Mathematics in the Sciences in Leipzig (Germany) in 2005. Since 2012 Hayk works in China, first at XJTLU, and from 2015 at the University of Nottingham Ningbo China. PDEs with geometric features, particularly free boundary and free discontinuity problems, are of his research interest. Among awards one could mention the NSFC research grant and the Lord Dearing teaching award.