On the kinetic Fokker-Planck equation in bounded domains

Analysis Seminar
Topic:On the kinetic Fokker-Planck equation in bounded domains
Speaker:Juhi Jang
Affiliation:University of Southern California; von Neumann Fellow, School of Mathematics
Date:Wednesday, April 27
Time/Room:4:30pm - 5:30pm/S-101

I will discuss the Kolmogorov equation, a simplest kinetic Fokker-Planck equation in the presence of boundaries. In the case of an absorbing boundary, I will present the well-posedness theory of classical solutions and Holder continuity of such solutions near the singular set. In the case of a reflecting boundary, there exists a critical exponent indicating different behavior of solutions depending sub/super critical regimes. I will show the role of the critical exponent and the singular set in the context of uniqueness and non-uniqueness of solutions to the Fokker-Planck equation.