报 告 人：周斌副教授（北京大学）

报告时间：2021年4月1号 下午2点

报告地点：腾讯会议（会议 ID：842 725 338）

摘要: We study the solvability of the second boundary value problem for a class of highly singular fourth order equations of Monge-Ampere type. They arise in the approximation of convex functionals subject to a convexity constraint using Abreu type equations. Both the Legendre transform and partial Legendre transform are used in our analysis. In two dimensions, we establish global solutions to the second boundary value problem for highly singular Abreu equations where the right hand sides are of $q$-Laplacian type for all $q>1$. We show that minimizers of variational problems with a convexity constraint in two dimensions that arise from the Rochet-Chone model in the monopolist's problem in economics with $q$-power cost can be approximated in the uniform norm by solutions of the Abreu equation for a full range of $q$.

报告人简介：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。2012年获得澳大利亚基金会Discovery Early Career Research Award奖，2018年获得国家优秀青年基金资助。