Liouville type equation with Neumann boundary condition and with singular data
发布人: 曹思圆   发布时间: 2018-09-29   浏览次数: 10

报告人:周春琴(上海交通大学 教授)
时间:10月11日 14:00-15:00

摘要:In this talk we will talk about the blow-up behaviors of solutions to the singular Liouville type equation with exponential Neumann boundary condition. We generalize the Brezis-Merle type concentration-compactness Theorem to this  Neumann problem. Then along the line of the  Li-Shafrir  type quantization property  we show that the blow-up value $m(0) \in 2\pi\N \cup \{ 2\pi(1+\alpha)+2\pi (\N\cup \{0\})\}$ if the singular point $0$ is a blow-up point.  In the end, when the boundary value of solutions has an additional condition, we can obtain the precise blow-up value $m(0)=2\pi(1+\alpha)$.