article

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

Authors: Hyung ju Hwang, Juhi Jang and Jaewoo Jung

Issue: Volume 64 (2015), Issue 6, 1767-1804

Abstract:

$We establish a well-posedness theory of classical solutions of the Fokker-Planck equation---the forward Kolmogorov equation in the half-space $\mathbb{R}^3_{+}$ 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 $L^{\infty}$ estimates. We prove the hypoellipticity up to the boundary away from the singular set, and moreover, we show that the solutions are H\"older continuous up to the singular set.$