Yuzhe Zhu : Smoothness property of hypoelliptic kinetic equations near boundaries

Posted by Roman Shvydkoy , part of the Analysis and Applied Mathematics Seminar.

At

Sept. 30, 2024, 4 p.m.

In

636 SEO

Abstract

The boundary regularization effect for hypoelliptic kinetic equations is limited. The solution with the simplest zero inflow boundary conditions exhibits at most Hölder continuity near the singular set of the boundary. We will discuss recent results on hypoelliptic regularity and explain the smoothness properties of solutions in the presence of boundary conditions in certain cases.