A Schiffer-type problem with applications to stationary Euler flows
数学专题报告
报告题目(Title)：A Schiffer-type problem with applications to stationary Euler flows
报告人(Speaker)：Antonio Fernandez (Universidad Autónoma de Madrid)
地点(Place)：ZoomID: 975 0876 4296, PWD: 583722
时间(Time)：2024 年 2月 29日 16：00—17：00
邀请人(Inviter)：熊金钢
报告摘要
If on a smooth bounded domain \(\Omega\subset\mathbb{R}^2\) there is a nonconstant Neumann eigenfunction \(u\) that is locally constant on the boundary, must \(\Omega\) be a disk or an annulus? This question can be understood as a weaker analog of the well-known Schiffer conjecture, in that the function \(u\) is here allowed to take a different constant value on each connected component of \(\partial \Omega\) yet many of the known rigidity properties of the original problem are essentially preserved. In this talk we provide a negative answer by constructing a family of nontrivial doubly connected domains \(\Omega\) with the above property. Then, we will show how our construction implies the existence of continuous, compactly supported stationary weak solutions to the 2D incompressible Euler equations which are not locally radial. The talk is based on a joint work with Alberto Enciso, David Ruiz and Pieralberto Sicbaldi.
* This PDE seminar is co-organized with Tianling Jin at The Hong Kong University of Science and Technology. See the seminar webpage:
https://www.math.hkust.edu.hk/~tianlingjin/PDEseminar.html
