Abstract. We consider the insulated conductivity problem with closely spaced inclusions in a bounded domain in R^n. The gradient of solutions may blow up as the distance between inclusions approaches to 0. Recently, we solved an outstanding open problem by obtaining an optimal gradient estimate of solutions in terms of the distance. This is based on joint work with Yanyan Li (Rutgers University) and Zhuolun Yang (ICERM at Brown University).
 

Bio. 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.