摘要： This is an summary talk for Moser-Trudinger inequality. In this talk, I first introduce the classical Moser-Trudinger inequalities in bounded domain and unbounded domain. Then I will present the work on the existence and no-existence for extremals of Moser-Trudinger inequality. The Trace-type Moser-Trudinger inequality in bounded and unbounded domain will be also discussed in this talk. Finally, if the time is permitted, some new development including uniqueness and quantization analysis theory for local Moser-Trudinger equation, multiplicity and supercritical non-local Moser-Trudinger equation will be introduced.

报告人简介：陈露，北京理工大学数学与统计学院副研究员。2018年博士毕业于北京师范大学，2019年在意大利比萨高师访问Andrea Malchiodi教授。主持国家自然科学基金青年和面上项目各一项。主要研究领域为几何泛函不等式与非线性椭圆偏微分方程，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。

邀请人：邹文明 教授