讲座题目：Solutions of the Minimal Surface Equation and of the Monge-Ampere Equation near Infinity

讲座报告人：韩青

讲座地点：腾讯会议   会议 ID：707 245 660

讲座时间：2020.09.25（周五） 上午9:30

参加对象：4556银河国际在线全体师生

主办单位：研究生院

承办单位：4556银河国际在线

报告人简介：韩青，美国圣母大学数学系教授。美国纽约大学库朗数学研究所博士，美国芝加哥大学博士后，曾在德国莱比锡马普所和美国纽约大学库朗数学研究所进行科研。获美国Sloan Research Fellowship. 韩青教授长期致力于非线性偏微分方程和几何分析的研究工作，在等距嵌入、Monge-Ampere方程、调和函数的零点集和奇异集、退化方程等方面做出了一系列原创性的重要研究成果

主讲内容：Classical results assert that, under appropriate assumptions, solutions near infinity are asymptotic to linear functions for the minimal surface equation and to quadratic polynomials for the Monge-Ampere equation for dimension n at least 3, with an extra logarithmic term for n=2. We characterize remainders in the asymptotic expansions the difference between solutions and linear functions and the difference between solutions and quadratic polynomials for the Monge-Ampere equation by a single function, which is given by a solution of some elliptic equation near the origin via the Kelvin transform. Such a function is smooth in the entire neighborhood of the origin for the minimal surface equation in every dimension and for the Monge-Ampere equation in even dimension, but only C^{n-1,/alpha} for the Monge-Ampere equation in odd dimension, for any /alpha in (0,1).