PDEA Seminar: Optimal regularity for kinetic equations in domains

Abstract: In this talk I will discuss the regularity of solutions to linear kinetic Fokker-Planck equations in domains with specular reflection condition. These models arise as linearizations of the Landau equation. While the interior regularity of such equations is well understood, the solution behavior near the boundary has remained open, even in the simplest case of Kolmogorov's equation. I will also mention recent results on other physical boundary conditions such as diffuse reflection and in-flow. This talk is based on joint works with Xavier Ros-Oton and Kyeongbae Kim.

This is a seminar in the PDEs and Applications seminar series.