  Recent result [Wu and Guo, Comm. Math. Phys., 2015] has shown that over the
2D unit disk, the classical half-space equation (CHS) for the neutron transport
does not capture the correct boundary layer behaviour as long believed. In this
paper we develop a regularization technique for CHS to any arbitrary order and
use its first-order regularization to show that in the case of the 2D unit
disk, although CHS misrepresents the boundary layer behaviour, it does give the
correct boundary condition for the interior macroscopic (Laplace) equation.
Therefore CHS is still a valid equation to recover the correct boundary
condition for the interior Laplace equation over the 2D unit disk.
