Schauder estimates for parabolic equations with degenerate or singular weights

We establish some C-0,C-alpha and C-1,C-alpha regularity estimates for a class of weighted parabolic problems in divergence form. The main novelty is that the weights may vanish or explode on a characteristic hyperplane Sigma as a power a > -1 of the distance to Sigma. The estimates we obtain are sharp with respect to the assumptions on coefficients and data. Our methods rely on a regularization of the equation and some uniform regularity estimates combined with a Liouville theorem and an approximation argument. As a corollary of our main result, we obtain similar C-1,C-alpha estimates when the degeneracy/singularity of the weight occurs on a regular hypersurface of cylindrical type.