Recent Progress on Stable Solutions of the Allen-Cahn Equation
数学专题报告
报告题目(Title)：Recent Progress on Stable Solutions of the Allen-Cahn Equation
报告人(Speaker)：Joaquim Serra (ETH)
地点(Place)：ZOOM ID: 990 3365 0021 PWD: 075159
时间(Time)：2025年11月6日（周四）16:00-17:00
邀请人(Inviter)：熊金钢
报告摘要
I will present recent results and open problems concerning stable solutions of the Allen-Cahn equation and its free boundary version. In particular, I will discuss the long-standing problem of classifying stable solutions to the Allen-Cahn equation, both with and without area bounds, in low dimensions, and the consequences of these classifications. I will outline the classical results and highlight more recent developments, emphasizing the main difficulties in the problem and some of the key ideas underlying the proofs of our recent results. The talk is based on two papers: one joint with Chan, Figalli, and Fernández-Real, and another joint with Florit and Simon.
* This PDE seminar is co-organized with Tianling Jin at HKUST and Juncheng Wei at CUHK. See the seminar webpage: https://www.math.hkust.edu.hk/~tianlingjin/PDEseminar.html
