Multi-bubble analysis for the Brezis-Nirenberg problem
数学专题报告
报告题目(Title)：Multi-bubble analysis for the Brezis-Nirenberg problem
报告人(Speaker)：Paul Laurain (Universite Gustave Eiffel)
地点(Place)：ZOOM ID: 934 2237 4331 PWD：644054
时间(Time)：2025 年 9月 18日 16：00-17：00
邀请人(Inviter)：熊金钢
报告摘要
In a celebrated paper, Brezis and Nirenberg showed that the behavior of the Yamabe-type equation $$\Delta u + a u = u^{2^*-1},$$ where $2^*$ is the critical Sobolev exponent, can vary dramatically depending on the data of the problem. In particular, there is a notion of a critical potential $a$, below which no positive solution exists. We are interested in the behavior of solutions as the potential approaches this critical value. We will examine how the location and rate of blow-up of these solutions are constrained by the Robin function of the operator $\Delta + a$. This is joint work with Tobias König.
* 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
