报告题目 (Title)：高阶Hardy-Sobolev-Mazya不等式极值的存在性
报告人 (Speaker)：陶春霞 副教授（北京工商大学）
报告时间 (Time)：2026年3月26日（周四）15:00
报告地点 (Place)：校本部 GJ403
邀请人(Inviter)：赵发友
主办部门：理学院 数学系
报告摘要：In this talk, we will first recall some sharp geometric inequalities and their extremals. Then we will present our recent progress on the existence of extremals for Hardy-Sobolev-Maz’ya inequalities (HSM) on the upper-half space. We develop the dual theory of minimizing sequence, the concentration-compactness principle for radial function on the hyperbolic setting, which combined with Helgason-Fourier analysis and the Riesz rearrangement inequality on the hyperbolic space, resolves the lack of compactness. As an application, we also obtain the existence and symmetry of the positive solution for the high order critical Brezis-Nirenberg equation on the entire hyperbolic space.
