Optimal regularity for kinetic equations in domains
数学专题报告
报告题目(Title)：Optimal regularity for kinetic equations in domains
报告人(Speaker)：Marvin Weidner (University of Bonn)
地点(Place)：ZOOM ID: 992 0251 2373 PWD：129157
时间(Time)：2025 年 9月 4日 （周四）16：00-17：00
邀请人(Inviter)：熊金钢
报告摘要
The Boltzmann equation is one of the central equations in statistical mechanics and models the evolution of a gas through particle interactions. In recent years, groundbreaking work by Imbert and Silvestre has led to a conditional regularity theory for periodic solutions of the Boltzmann equation. They established that any possible singularity of a periodic solution to the Boltzmann equation must be visible macroscopically. A major open challenge is whether such a theory can be extended to bounded domains with physically relevant boundary conditions.
As a first step toward understanding the boundary case, in this talk I will discuss the smoothness of solutions to linear kinetic Fokker-Planck equations in domains with specular reflection condition. While the interior regularity of such equations is well understood, their behavior near the boundary has remained open, even in the simplest case of Kolmogorov's equation. Finally, I will report on recent joint work with Xavier Ros-Oton, in which we establish sharp boundary regularity results for this class of equations.
* This PDE seminar is co-organized with Tianling Jin at HKUST and Juncheng Wei at CUHK. See the seminar webpage: https://www.math.hkust.edu.hk/~tianlingjin/PDEseminar.html
