Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	陈露,北理工
Inviter:	张翼
Title:	Uniqueness and quantization analysis for positive solutions of Trudinger-Moser equation
Language:	Chinese
Time & Venue:	2023.08.14 14:00-16:00 思源楼S813
Abstract:	In this talk, I will first introduce our uniqueness result for positive solutions of Trudinger-Moser equation in unit ball of Euclidean space or Hyperbolic space, this result can be seen as an important step for the uniqueness of maximizers of Trudinger-Moser inequalities. Based on this uniqueness result, we will develop a new strategy to establish the quantization property of elliptic equations with the critical exponential growth in the balls of hyperbolic spaces, and obtain the multiplicity and non-existence of positive critical points for super-critical Trudinger-Moser functional. Our method for the quantization property and non-existence of the critical points avoids using the complicated blow-up analysis used in the literature. This is a joint work with Prof. Lu from Connecticut University and Prof. Zhu from Jiangsu Univerity.