Sharp quantitative stability for fractional Sobolev inequalities and the Yamabe problem under bubbling

发布时间：2024-11-18 作者：浏览次数：

Speaker:	陈海霞	DateTime:	2024年11月21日（周四）下午 15：00-16：00
Brief Introduction to Speaker: 博士毕业于华中师范大学，博士期间曾在意大利罗马第一大学联合培养，目前在韩国汉阳大学进行博士后研究。主要研究方向是非线性椭圆型偏微分方程、非线性泛函分析，已在JFA, Nonlinearity等期刊上发表多篇学术论文。曾担任过国际期刊NoDEA和Phys. D 审稿人。		Place:	腾讯会议：206-422-388
Abstract: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.