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Solutions of the Minimal Surface Equation and of the Monge-Ampere Equation near Infinity-韩青教授

作者:   来源:  时间:2020-09-24

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

报告人:韩青  教授(美国圣母大学)

Abstract:

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).

 

时间:2020年9月24日(周四)  上午9:00-10:00

地点:线上腾讯会议(会议号:473 452 822)

联系人:张振雷

 

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