Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	欧乾忠教授，广西师范大学
Inviter:	叶剑
Title:	Classification of solutions to the Yamabe equation in R^n
Language:	Chinese
Time & Venue:	2023.07.17 09:00-10:00 南楼N802
Abstract:	In this talk, I will focus on the classification of positive solutions to the Yamabe equation, i.e., the critical semilinear elliptic equation $-\Delta u=u^{\frac{n+2}{n-2}}$ , in $R^n(n>1)$. It is well known that such issue is crucial in many applications such as a priori estimates, blow-up analysis and asymptotic analysis. Note that this equation has 2-parameters family of solutions which are classified by Caffarelli-Gidas-Spruck [CPAM1989] , via the method o f moving planes. I will present a new proof of this result in lower dimensions, by exploiting the method of integral estimate.