講座編號：jz-yjsb-2020-y013
講座題目：Solutions of the Minimal Surface Equation and of the Monge-Ampere Equation near Infinity
主 講 人：韓 青 美國圣母大學(xué)
講座時間：2020年09月25日（星期五）上午09:30
講座地點(diǎn)：線上平臺：騰訊會議，會議ID: 707 245 660
參加對象：數(shù)學(xué)與統(tǒng)計學(xué)院全體師生
主辦單位：研究生院
承辦單位：數(shù)學(xué)與統(tǒng)計學(xué)院
主講人簡介：
韓青，美國圣母大學(xué)數(shù)學(xué)系教授。美國紐約大學(xué)庫朗數(shù)學(xué)研究所博士，美國芝加哥大學(xué)博士后，曾在德國萊比錫馬普所和美國紐約大學(xué)庫朗數(shù)學(xué)研究所進(jìn)行科研。獲美國Sloan Research Fellowship. 韓青教授長期致力于非線性偏微分方程和幾何分析的研究工作，在等距嵌入、Monge-Ampere方程、調(diào)和函數(shù)的零點(diǎn)集和奇異集、退化方程等方面做出了一系列原創(chuàng)性的重要研究成果。
主講內(nèi)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).