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：欧乾忠 教授（广西师范大学）
题 目：Classification of solutions to the Yamabe equation in R^n
时 间：2023.07.17（星期一）9:00-10:00
地 点：数学院南楼N802
摘 要：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.
报告人：吴汪哲 博士（中国科学技术大学）
题 目：Liouville theorem for one kind of quasilinear elliptic equations
时 间：2023.07.17（星期一）10:00-11:00
地 点：数学院南楼N802
摘 要：We study the positive solutions of the equation $-\Delta u=N u^p + M |\nabla u|^q$ and deduce one Liouville type theorem for the global solutions in the critical and subcritical cases, which improves the results of Bidaut-Véron, Garcia-Huidobro and Véron. This work is joint with Xi-nan Ma and Qiqi Zhang.
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