  We establish Schauder a priori estimates and regularity for solutions to a
class of boundary-degenerate elliptic linear second-order partial differential
equations. Furthermore, given a smooth source function, we prove regularity of
solutions up to the portion of the boundary where the operator is degenerate.
Degenerate-elliptic operators of the kind described in our article appear in a
diverse range of applications, including as generators of affine diffusion
processes employed in stochastic volatility models in mathematical finance,
generators of diffusion processes arising in mathematical biology, and the
study of porous media.

Analysis of PDEs;Probability;Computational Finance;Pricing of Securities