题    目：Sharp quantitative stability for the Yamabe problem and fractional Sobolev inequalities

主讲人：陈海霞

单    位：韩国汉阳大学

时    间：2024年12月25日 20:00

腾讯ID：497-543-979

摘    要：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 Yamabe problem and the fractional Lane-Emden equation of all possible orders.

简    介：陈海霞, 韩国汉阳大学博士后（2023年6月至今）。2017年9月-2022年12月在华中师范大学硕博连读，博士期间曾在意大利罗马第一大学联合培养。目前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。