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--- 分析与偏微分方程讨论班(2024春季第01讲)

The decay estimates of higher order elliptic operator

尧小华 （华中师范大学）

时间：04月03日（周三）下午14:30-15:30

地点：#腾讯会议：509-766-8696 会议密码：654321

点击链接直接加入会议：

https://meeting.tencent.com/p/5097668696

摘要: Th $L^p$ decay estimates of Schr\”odinger operators are interesting topics, which play fundamental roles in the wellposedness of nonlinear dispersive equations and the (asymptotic) stability of solitary waves. In this talk, I will review some recent works on the time decay estimates of the higher order elliptic operators (poly-harmonic type) with the decay potentials. The main techniques based on the detailed analysis of free resolvent and spectral perturbation, where the classifications of zero resonances and zero asymptotic expansions of resolvent are the most important parts, which are indispensable to establish all kinds of dispersive results with general potentials.

报告人简介: 尧小华，华中师范大学数学与统计学学院教授，博士生导师；2010年入选教育部新世纪人才支持计划，主要从事调和分析与微分算子的研究，围绕薛定谔算子的色散估计、孤立子的稳定性等问题开展科研工作，论文发表在Comm. Math. Phys.、Trans.  AMS.、Ann. H. Poincare、J. Funct. Anal.等国际数学期刊上；目前连续主持国家基金委面上项目3项，曾主持教育部重点项目1项，参与了教育部偏微分方程CJ学者创新团队的建设。学术上先后访问过美国Johns Hopkins大学、普林斯顿高等研究所、新泽西罗格斯大学等高校。

邀请人：张安

欢迎大家参加！