报告人：周斌（北京大学）

邀请人：张宁

报告时间：2022年5月18日 （星期三）14: 00-16:00  

报告地点：腾讯会议：771 5980 3545

报告题目：Regularity of the complex Monge-Ampére equation and Moser-Trudinger type inequalities

报告摘要：A fundamental problem for the complex Monge-Ampére equation is to establish the a priori estimates of solutions when the right hand side f is not smooth. A breakthrough was made by Kolodziej, who obtained the L^\infty-estimate when f is in L^p with p>1. It was later shown that the solution is Hölder continuous when the domain is smooth and strictly pseudo-convex, and the boundary value is Hölder continuous. These results were built upon the pluripotential theory.  In this talk, we will discuss a pure PDE approach to the regularity of the complex Monge-Ampére equation, based on the related Moser-Trudinger type inequalities. More generally, we will also discuss the relations between trace inequalities(Sobolev and Moser-Trudinger type), isocapacitary inequalities and the regularity of the complex Hessian and Monge-Ampére equations when the right hand side is a general positive Borel measure.

报告人简介：周斌，北京大学数学学院副教授，博士生导师，主要从事复几何，几何分析和完全非线性方程的研究。