Selfduality and the Kinetic Fokker--Planck Equation with Dirichlet Data
Abstract
I use selfdual variational calculus to establish well-posedness of the Dirichlet problem for the kinetic Fokker--Planck equation with data on the incoming boundary. The selfdual approach -- initiated by Brezis-Ekeland in 1976 and developed in my book in 2008 -- was attempted earlier (and verified in dimension one) by Armstrong and Mourrat. With the assistance of my new friend Claude, who -- among other things -- led me to old papers of Kolmogoroff (1934) and McKean (1963), I will outline a proof of well-posedeness in higher dimensions.