报告题目：Recent progress of the perfect and insulated conductivity problems

报告人：董弘桀

报告时间：2023年12月06日（周三）09:30开始

报告地点：腾讯会议（388-619-397）

报告摘要：In the first part of the talk, I will present our work about the insulated conductivity problem with closely spaced inclusions in a bounded domain in $R^n$. A noteworthy phenomenon in this context is the potential for the gradient of solutions to blow up as the distance between inclusions tends to zero.We obtained an optimal gradient estimate of solutions in terms of the distance, which settled down a major open problem in this area. In the second part, I will discuss recent results about the insulated and perfect conductivity problems when the current-electric field relation is a power law. Based on joint work with Yanyan Li (Rutgers University), Zhuolun Yang and Hanye Zhu (Brown University).

报告人简介：Hongjie Dong is a Professor at the Division of Applied Mathematics of Brown University. He received his Ph.D. in 2005 at the Department of Mathematics in the University of Minnesota. Prof. Dong's current research interests include Partial Differential Equations, Probability, and Numerical Analysis. He was the recipient of an NSF early career award in 2011 and a Simons fellowship in 2021. He has also been on the editorial boards of several journals including SIAM J. Math. Anal. and J. Differential Equations.