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：Hongjie Dong (Brown univeristy)
题 目：Sobolev and Schauder estimates for degenerate Kolmogorov equations
时 间：2023.07.03（星期一）09:30-10:30
地 点：思源楼S813
摘 要：I will present some recent results about degenerate (ultra-parabolic) Kolmogorov equations (also known as linear kinetic Fokker–Planck equations) with rough coefficients. Such equations appear often in kinetic theory. We consider equations in both divergence and non-divergence form and our proof does not rely on any kernel estimates.
This is based on joint work with Timur Yastrzhembskiy (Brown University).
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题 目：Recent results about the insulated conductivity problem
时 间：2023.07.03（星期一）10:30-11:30
地 点：思源楼S813
摘 要：In the first part of the talk, I will present our results about 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. 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 a recent result about the insulated conductivity problem when the current-electric field relation is a power law.
Based on joint work with Yanyan Li (Rutgers University), Zhuolun Yang (ICERM, Brown University), and Hanye Zhu (Brown University).
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