  The paper considers a class of linear Boltzmann transport equations which
models a charged particle transport. The equation is an approximation of the
original exact transport equation which involves hyper-singular integrals in
their collision terms. Hyper-singular integrals can be approximated by partial
differential operators together with partial integral operators which leads to
an approximation under consideration. This type of approximation is applied,
for example in the dose calculation of radiation therapy. The related transport
problem is an initial inflow boundary value problem. Regularity results of
solutions are verified utilizing the scales of relevant anisotropic Sobolev
spaces.
