偏微分方程研讨班：C1,1/3− very weak solutions to the two dimensional Monge–Ampère equation

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：曹文涛 研究员（首都师范大学）   

题  目：C^1,1/3−  very weak solutions to the two dimensional Monge–Ampère equation

时  间：2023.11.23（星期四）上午11:00-12:00

地  点：思源楼S813

摘 要：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.