中科院数学与系统科学研究院

数学研究所

学术报告

偏微分方程研讨班

报告人： 周斌（北京大学）   

题  目：Singular Abreu equations and linearized Monge-Ampère equations with drifts

时  间：2023.05.17（星期三）15:00-16:00

地  点：腾讯会议：896-246-072

摘  要：We study the solvability of singular Abreu equations which arise in the approximation of convex functionals subject to a convexity constraint. Previous works established the solvability of their second boundary value problems either in two dimensions, or in higher dimensions under either a smallness condition or a radial symmetry condition. Here, we solve the higher dimensional case by transforming singular Abreu equations into linearized Monge-Ampère equations with drifts. We establish global Hölder estimates for the linearized Monge-Ampère equation with drifts under suitable hypotheses, and then use them to the regularity and solvability of the second boundary value problem for singular Abreu equations in higher dimensions. Many cases with general right-hand side will also be discussed.

个人简介：周斌，北京大学数学学院研究员，博士生导师，主要从事复几何，几何分析和完全非线性方程的研究。2012年获得澳大利亚基金会Discovery Early Career Research Award奖，2018年获得国家优秀青年基金资助。