Analysis Seminar

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.