偏微分方程研讨班:Uniqueness and quantization analysis for positive solutions of Trudinger-Moser equation

中科院数学与系统科学研究院

数学研究所

学术报告

偏微分方程研讨班

报告人：陈露（北理工） 
题  目：Uniqueness and quantization analysis for positive solutions of Trudinger-Moser equation
时  间：2023.08.14（星期一）14:00-16:00
地  点：思源楼S813
摘  要：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.