文摘
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 1" class="mathmlsrc">1-s2.0-S0022123616303184&_mathId=si1.gif&_user=111111111&_pii=S0022123616303184&_rdoc=1&_issn=00221236&md5=b37118c85de3dde2f68883dab0dbdb46" title="Click to view the MathML source">C0-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.