Higher order Schauder estimates for parabolic equations with degenerate or singular weights

In this paper, we complete the analysis initiated in [AFV24] establishing some higher order Ck+2,α Schauder estimates (k ∈ N) for a a class of parabolic equations with weights that are degenerate/singular on a characteristic hyperplane. The C2,α-estimates are obtained through a blow-up argument and a Liouville theorem, while the higher order estimates are obtained by a fine iteration procedure. As a byproduct, we present two applications. First, we prove similar Schauder estimates when the degeneracy/singularity of the weight occurs on a regular hypersurface of cylindrical type. Second, we provide an alternative proof of the higher order boundary Harnack principles established in [BG16,Kuk22].