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NCTS International Geometric Measure Theory Seminar
 
22:30 - 23:30, January 20, 2021 (Wednesday)
Microsoft Teams, Online seminar
(線上演講 微軟 共同作業軟體)
Second Order Estimates for Interfaces of Allen-Cahn
Juncheng Wei (University of British Columbia)

In this talk,  I will discuss a uniform estimate for level sets of stable solutions to the singularly perturbed Allen-Cahn equation in dimensions (which is optimal). The proof combines two ingredients: one is a reverse application of the infinite dimensional Lyapunov-Schmidt reduction method which enables us to reduce the estimate for these level sets to a corresponding one on solutions of Toda system; the other one uses a small regularity theorem on stable solutions of Toda system to establish various decay estimates, which gives a lower bound on distances between different sheets of solutions to Toda system or level sets of solutions to Allen-Cahn equation. (Joint work with Kelei Wang.)

Registration through the seminar website https://sites.google.com/ncts.ntu.edu.tw/international-gmt-seminar required.



 

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