学术报告会：C1,1/3−very weak solutions to the two dimensional Monge–Ampère equation

报告题目：C1,1/3−very weak solutions to the two dimensional Monge–Ampère equation

报 告 人： 曹文涛 （首都师范大学  研究员）

报告时间：2024年10月14日周一09：00

腾讯会议ID：617-161-408

Abstract：For any θ<1/3 , we show that very weak solutions to the two-dimensional Monge–Ampère equation with regularity C1,θ are dense in the space of continuous functions. This result is shown by a convex integration scheme involving a subtle decomposition of the defect at each stage. The decomposition diagonalizes the defect and, in addition, incorporates some of the leading-order error terms of the first perturbation, effectively reducing the required amount of perturbations to one。This is a joint work with Jonas Hirsch and Dominik Inauen from Leipzig Univerisity.

个人简介：

曹文涛，首都师范大学交叉科学研究院研究员。2021年入选国家海外高层次人才计划青年项目。2017年获得中科院优秀博士学位论文奖。主要研究微分几何中等距嵌入和双曲守恒律方程组，在Arch. Ration. Mech. Anal.、J. Funct. Anal., SIAM J. Math. Anal., Comm. Partial Differential Equations 等重要学术期刊上发表论文20余篇。