报告时间：2026年9月18日 9:00开始

报 告 人：闫绪恺（俄克拉荷马州立大学数学系副教授）

报告地点：腾讯会议：566-696-530

报告题目：Anisotropic Caffarelli-Kohn-Nirenberg type inequalities

报告摘要：Caffarelli, Kohn and Nirenberg established in 1984 a family of weighted Sobolev-type interpolation inequalities with isotropic weights. These inequalities are generalizations of Gagliardo-Nirenberg-Sobolev inequalities and Hardy's inequalities, and have been extensively studied in various aspects. In this talk, I will discuss some extensions of these inequalities with anisotropic weights. I will first make an overview about the development and related problems on Gagliardo-Nirenberg-Sobolev inequalities and Caffarelli-Kohn-Nirenberg inequalities. I will talk about some recent study on extensions of these inequalities with different types of weights and related questions. I will also present a more general anisotropic version of CKN inequalities, and discuss an application of them in the study of Navier-Stokes equations. This talk is based on joint works with Yanyan Li.

报告人简介：闫绪恺，美国俄克拉荷马州立大学数学系副教授。其在中国科学技术大学取得学士学位，随后于美国罗格斯大学取得博士学位，并在佐治亚理工大学从事博士后研究。2020年至今就职于俄克拉荷马州立大学。主要从事非线性偏微分方程的研究。其论文发表于CPAM, Adv. Math., ARMA, JFA, CVPDE等杂质发表多篇论文。于2025年获得美国国家自然科学基金NFS CAREER Award。