偏微分方程研讨班:Annealed Calderon-Zygmund estimates for elliptic operator with random coefficients on C2 domains

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：徐强 副教授（兰州大学）

题  目：Annealed Calderon-Zygmund estimates for elliptic operator with random coefficients on C² domains

时  间：2023.12.04（星期一）11:00-12:00

地  点：思源楼S813

摘  要：Concerned with elliptic operators with stationary random coefficients of integrable correlations and bounded C² domains, this paper mainly studies annealed Calder\'on-Zygmund estimates, which is new even for constant coefficients. Stronger than some classical results derived by a perturbation argument in the deterministic case, our result owns a scaling-invariant property, which additionally requires a non-perturbation argument recently developed by M. Jeosen and F. Otto [JFA,22']. To handle boundary estimates, we have to introduce boundary correctors to treat for an optimal estimate from suboptimal. For the weighted estimates, we hand over the proof to Shen's real arguments. The most attractive part of the paper is to show how these two powerful real methods work together to make the result clean and robust.

个人简介：徐强，兰州大学数学与统计学院 副教授。2016年在兰州大学获得博士学位，先后获得北京大学数学学院、德国马普所博士后职位。其主要工作集中于均匀化理论的量化研究。在CVPDE、JDE、SIAM J.Math Anal等杂志发表论文多篇。