R440, Astronomy-Mathematics Building, NTU
(台灣大學天文數學館 440室)
Regularity of Mumford-Shah minimizers at the crack-tip
Hayk Mikayelyan (University of Nottingham Ningbo China)
We consider the Mumford-Shah functional in the plain and study the asymptotics of the solution near the crack-tip. This problem arise in certain models of fracture mechanics. 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. (joint work with John Andersson and Zhilin Li)
