On the kinetic Fokker-Planck equation in the half-space with absorbing barriers Hyung HwangJuhi JangJaewoo Jung 35Q8435G1635H10Fokker-PlanckIntial-boundary value problemHypoellipticityExponential decay 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. Indiana University Mathematics Journal 2015 text pdf 10.1512/iumj.2015.64.5679 10.1512/iumj.2015.64.5679 en Indiana Univ. Math. J. 64 (2015) 1767 - 1804 state-of-the-art mathematics http://iumj.org/access/