On the kinetic Fokker-Planck equation in the half-space with absorbing barriers

Abstract

We establish a well-posedness theory of classical solutions of the Fokker-Planck equation-the forward Kolmogorov equation in the half-space R-+(3) with absorbing boundary conditions. We first build a theory for the regularized equations near the singular set by the method of characteristics, and then pass to the limit by uniform L-1 and L-infinity estimates. We prove the hypoellipticity up to the boundary away from the singular set, and moreover, we show that the solutions are Holder continuous up to the singular set.