  We study the boundary regularity properties and derive a priori pointwise
supremum estimates of weak solutions and their derivatives in terms of suitable
weighted $L^2$-norms for a class of degenerate parabolic equations that satisfy
homogeneous Dirichlet boundary conditions on certain portions of the boundary.
Such equations arise in population genetics in the study of models for the
evolution of gene frequencies. Among the applications of our results is the
description of the structure of the transition probabilities and of the hitting
distributions of the underlying gene frequencies process, which correspond to
the fundamental solution and the caloric measure of the parabolic equation,
respectively.
