Higher order Schauder estimates for degenerate or singular parabolic equations
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912440530239488 |
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| author | Audrito, Alessandro Fioravanti, Gabriele Vita, Stefano |
| author_facet | Audrito, Alessandro Fioravanti, Gabriele Vita, Stefano |
| contents | In this paper, we complete the analysis initiated in [AFV24] establishing some higher order $C^{k+2,α}$ Schauder estimates ($k \in \mathbb{N}$) for a a class of parabolic equations with weights that are degenerate/singular on a characteristic hyperplane. The $C^{2,α}$-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]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_08575 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Higher order Schauder estimates for degenerate or singular parabolic equations Audrito, Alessandro Fioravanti, Gabriele Vita, Stefano Analysis of PDEs 35B65, 58J35, 35B44, 35B53 In this paper, we complete the analysis initiated in [AFV24] establishing some higher order $C^{k+2,α}$ Schauder estimates ($k \in \mathbb{N}$) for a a class of parabolic equations with weights that are degenerate/singular on a characteristic hyperplane. The $C^{2,α}$-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]. |
| title | Higher order Schauder estimates for degenerate or singular parabolic equations |
| topic | Analysis of PDEs 35B65, 58J35, 35B44, 35B53 |
| url | https://arxiv.org/abs/2403.08575 |