报告人：Hayk Mikayelyan(School of Mathematical Sciences, 宁波诺丁汉大学)
时 间：2019年4月26日 上午10：00---11：00
地 点：华南数学应用与交叉研究中心学术报告厅111
题目： Regularity of Mumford-Shah minimizers in 2D/3D at the crack-tip/crack-front.
摘要：
In the plain we derive the full asymptotics of the solution near the crack-tip. It is well-known that the leading term in the asymptotics at the crack-tip is related to the stress intensity factor. We calculate the higher order terms in the asymptotic expansion, and show that those are related to the curvature of the crack close to the tip. Moreover, we derive a new Euler-Lagrange condition for the minimizers. We also develop a new numerical method to compute the minimizers in 2D, which is the very accurate near the crack-tip. In 3D we construct a continuous family of stationary solutions which are not global minimizers. We also observe numerically that these functions are not local minimizers. We make a conjecture that the dependence of the function on the point running over the crack-front is related to the behaviour of the co-normal tangent at the crack-front. (joint work with John Andersson, Antoine Lemenant and Zhilin Li)