中科院数学与系统科学研究院
数学研究所
偏微分方程研讨班
报告人： 周斌 教授（北京大学）
题 目：Interior estimates for the Monge-Ampere typed fourth order equations
时 间：2021.12.13（星期一），16:00-17:00
地 点：数学院南楼N210室
摘 要：We first use the partial Legendre transform to obtain the interior regularity of a class of fourth order equations of Monge-Ampere type in dimension two. As an application, we obtain a new proof of the Bernstein theorems including the Chern conjecture on the affine maximal surfaces, without using Caffarelli-Gutierrez's estimate. In higher dimensions, we also obtain the interior regularity in terms of the integral bounds on the second derivatives and the inverse of the determinant.