题目（Title）：Singular Abreu equations and minimizers of convex functionals with a convexity constraint
报告人（Speaker）：Prof. Nam Q. Le（Indiana University）
报告时间（Time）：2020年9月18日下午 16：00（北京时间）
方式（Online）：ZOOM ID：680 4032 3158 （密码：624535 ）
摘要（Abstract）：Abreu type equations are fully nonlinear, fourth order, geometric PDEs which can be viewed as systems of two second order PDEs, one is a Monge-Ampere equation and the other one is a linearized Monge-Ampere equation. They first arise in the constant scalar curvature problem in differential geometry and in the affine maximal surface equation in affine geometry. This talk discusses the solvability and convergence properties of second boundary value problems of singular, fourth order equations of Abreu type arising from approximation of convex functionals whose Lagrangians depend on the gradient variable, subject to a convexity constraint. These functionals arise in different scientific disciplines such as Newton's problem of minimal resistance in Physics, the Rochet-Choné model of monopolist's problem in Economics, and variational problems arising in the analysis of wrinkling patterns in floating elastic shells in Elasticity. In particular, this talk explains how minimizers of the 2D Rochet-Choné model can be approximated by solutions of singular Abreu equations.
报告人简介：Nam Q. Le, 2008年在美国纽约大学柯朗研究所获得博士学位，现为美国印第安纳大学副教授。Nam Q. Le 长期从事偏微分方程、几何分析和变分法的研究，研究兴趣为Monge-Ampere方程、线性化Monge-Ampere方程、平均曲率流和Gamma收敛性及其应用。目前担任印第安纳大学数学杂志编委。在Invent. Math., Comm. Pure Appl. Math., Comm. Math. Phys. 和 Arch. Ration. Mech. Anal. 等国际高水平杂志上发表30余篇论文。2017年出版专著《Dynamical and Geometric Aspects of Hamilton-Jacobi and Linearized Monge-Ampere Equations》。
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数学与统计学院
2020年9月16日