Higher order Schauder estimates for degenerate or singular parabolic equations

Abstract

In this paper, we complete the analysis initiated in [AFV24] establishing some higher order $C^{k+2,\alpha }$ Schauder estimates ($k\in \mathbb{N}$) for a a class of parabolic equations with weights that are degenerate/singular on a characteristic hyperplane. The $C^{2,\alpha }$-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].

This is the final version of the paper published in Revista Matematica Iberoamericana. Compared to the previous version, the title of the paper has been changed

Cited by in corpus (1)

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