2026京师调和分析论坛(6) (2026.9.22)
会议安排
Zoom会议号：889 530 09805，入会密码：999999
时间 |
报告人 |
报告题目 |
单位 |
15:00-16:00 |
Rupert Frank |
Sharp Functional Inequalities and Their Stability (I) |
德国慕尼黑大学 |
16:10-16:40 |
Sharp Functional Inequalities and Their Stability (II) |
会议由以下项目支持:
北京师范大学教育部&科技部“调和分析及其应用创新引智基地”
国家自然科学基金重点项目“相关于球平均、Chirp函数和区域上算子的函数空间公理化实变理论及其应用”
组委会：戴峰, 杨大春, 袁文, 张阳阳
2026年9月7日
报告信息
报告题目: Sharp Functional Inequalities and Their Stability
报告摘要: The Sobolev inequality is a paradigmatic example of a functional inequality with many applications in the Calculus of Variations, Geometric Analysis and PDEs. In some of these applications the optimal value of the constant is of importance, as is a characterization of the set of optimizers. The stability question is whether functions whose Sobolev quotient is almost minimal are close to minimizers of the inequality and, if so, in which sense. We give a gentle introduction to this question and review some recent results on the Sobolev inequality and other functional inequalities of a similar nature. In the second part of this talk we discuss in more detail a stability result, obtained jointly with Dolbeault, Esteban, Figalli and Loss, that displays the optimal dependence on the dimension.
