We consider the boundary value problem of the stationary transport equation
in the slab domain of general dimensions. In this paper, we discuss the
relation between discontinuity of the incoming boundary data and that of the
solution to the stationary transport equation. We introduce two conditions
posed on the boundary data so that discontinuity of the boundary data
propagates along positive characteristic lines as that of the solution to the
stationary transport equation. Our analysis does not depend on the celebrated
velocity averaging lemma, which is different from previous works. We also
introduce an example in two dimensional case which shows that piecewise
continuity of the boundary data is not a sufficient condition for the main
result.Comment: 15 pages, no figure