Quantitative stability of Geometric functional inequality.

发布时间：2024-01-02 作者：浏览次数：

Speaker:	陈露	DateTime:	2024年1月9日（周二）上午10:00-11:00
Brief Introduction to Speaker: 陈露，北京理工大学长聘副教授，博导。2018年博士毕业于北京师范大学，在 Moser-Truding-Adams不等式的最佳常数和极值问题、几何不等式的量化稳定性，指数临界增长的薛定谔方程基态解、双曲空间上波方程的散射理论等方面取得了重要的进展，相关结果发表在Proc. Lond. Math. Soc.， Adv.Math, Trans. AMS, J. Funct. Anal，Rev. Mat. Iberoam等国际学术期刊。		Place:	6号楼2楼报告厅
Abstract:In this talk, we will first discuss the quantitative stability for the Hardy-Littlewood-Sobolev (HLS) inequalities. By establishing the relation between the stability of HLS inequalities and the stability of fractional Sobolev inequalities, we also give the quantitative stability of the fractional Sobolev inequalities. Finally, we also discuss the optimal asymptotic lower bound for fractional Sobolev inequality and Log Sobolev inequality on the sphere. Our proofs are based on the competing symmetries, the continuous Steiner symmetrization inequality for the HLS integral, complicated orthogonal estimate, and the dual stability theory. This talk is based on the joint work with Prof. Lu from Connecticut University and Prof. Tang from Beijing Normal University.