题目: Attainability of the best constant of Hardy-Sobolev inequalities with full boundary singularities

报告人: 孙黎明 (中国科学院数学与系统科学研究院)

时间: 2024年4月2日，周二下午，16:00-17:00

地点: 立德楼 709

腾讯会议: 680-734-613， 密码: 56223

摘要: We consider a type of Hardy-Sobolev inequality, whose weight is singular on the whole domain boundary. We are concerned with the attainability of the best constant of such inequality. In dimension two, we link it to a conformally invariant one using the conformal radius of the domain. The best constant of such inequality on a smooth domain is achieved if and only if the domain is non-convex. In higher dimensions, the best constant is achieved if the domain has negative mean curvature somewhere.

报告人简介: 孙黎明，博士毕业于美国罗格斯(Rutgers)大学，现任中国科学院数学与系统科学研究院副研究员。主要从事椭圆型偏微分方程和非线性泛函分析的研究。发表学术论文10余篇，其中部分成果发表于Duke Math. J., Adv. Math，JFA等学术刊物上。