报告题目：Fractional integral and differential operators

报 告 人：刘丽光

时 间：2024年11月23日（周六）下午 2：30-3：30

地 点：国交2号楼315会议室

简 介：We will talk about some recent analysis results on restricting principles of Riesz potentials (or, the fractional integral operator) $I_s$ as well as some applications to partial differential equations related to fractional differential operators $\{(-\Delta)^\frac s2, \nabla^s, \mathrm{div}^s\}$.

报告题目：Sharp quantitative stability for fractional Sobolev in…

报 告 人：陈海霞

时 间：2024年11月21日（周四） 下午 15：00-16：00

地 点：腾讯会议：206-422-388

简 介：The quantitative stability for sharp inequalities in analysis and geometry is a fascinating subject that has attracted many researchers for decades. Since the seminar works of Brezis and Lieb (1985), many results have appeared dealing with the properties of the Sobolev inequalities, their variants, harmonic maps, etc. In contrast, the quantitative stability for the solutions to the Euler-Lagrange equations induced by sharp inequalities has been less understood. Nonetheless, it was completely analyzed in a Hilbertian Sobolev setting recently, thanks to the contributions of Ciraolo et al. (2018 IMRN), Figalli and Glaudo (2020 ARMA), and Deng et al. (2024 DUKE). In this talk, I will introduce my recent works on quantitative stability, collaborated with S. Kim (Hanyang U.) and J. Wei (CUHK) for the fractional Lane-Emden equation of all possible orders and the Yamabe problem.

报告题目：几类临界问题的正规化解

报 告 人：唐先华

时 间：2024年11月24日（周日） 上午 10：30-11：30

地 点：国交2号楼315会议室

简 介：介绍临界情形下Schrodinger方程、 Schrodinger-Poisson 方程、Kirchhoff方程和双临界Choquard方程正规化解存在性结果和研究进展。