  We solve a Kolmogorov-type hypoelliptic parabolic partial differential
equation with a "side" boundary condition (in the direction of the weak
H\"ormander condition). We construct an approximate boundary potential which
captures the effect of the boundary condition. Integrals against this
approximate boundary potential have a novel discontinuity at the boundary. We
introduce some polynomial corrections to this approximate boundary potential
and then construct a boundary-domain Volterra equation to solve the original
partial differential equation. This Volterra integral equation is iteratively
solved, and the bounds contain a periodic behavior resulting from the boundary
effects.
