一、报告题目

Solvability of a class of singular fourth order equations of Monge-Ampere type

二、主讲人

周斌

三、报告时间

2021年11月4日 10:00–11:00

四、报告地点

腾讯会议ID : 151 881 701

五、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.

六、主讲人简介

周斌，北京大学数学科学学院副教授，博士生导师，“国家优秀青年科学基金”获得者。主要从事几何分析的研究，在Adv. Math., Ann. PDE，J. Funct. Anal., Cal. Var. PDEs，Int. Math. Res. Not.等国际著名期刊上发表论文20余篇。

七、主办单位

非线性期望前沿科学中心

数学与交叉科学研究中心