  Kimura diffusions serve as a stochastic model for the evolution of gene
frequencies in population genetics. Their infinitesimal generator is an
elliptic differential operator whose second-order coefficients matrix
degenerates on the boundary of the domain. In this article, we consider the
inhomogeneous initial-value problem defined by generators of Kimura diffusions,
and we establish $C^0$-estimates, which allows us to prove that solutions to
the inhomogeneous initial-value problem are smooth up to the boundary of the
domain where the operator degenerates, even when the initial data is only
assumed to be continuous.
