Analysis & Probability Seminar

Speaker: Lukas Niebel (University of Münster)
Title: Mollification in kinetic geometry
Abstract: In this talk, I will discuss one of the classical and most useful tools in analysis: mollification. After a brief recap of its role in elliptic and parabolic settings, I will turn to the kinetic setting and present a new approach to kinetic mollification, developed in joint work with Helge Dietert, Clément Mouhot, and Rico Zacher. I will explain how this form of kinetic mollification can be understood as averaging along critical kinetic trajectories. I will then describe several applications, including sharp Sobolev-type inequalities, scale-invariant transfer-of-regularity estimates, and new bounds in the kinetic De Giorgi–Nash–Moser theory.