Hölder regularity of solutions of degenerate parabolic equations of general dimension
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929611321901056 |
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| author | Jang, Hyo Seok Lee, Ki-Ahm |
| author_facet | Jang, Hyo Seok Lee, Ki-Ahm |
| contents | We establish the Alexandroff-Bakelman-Pucci estimate, the Harnack inequality, the Hölder regularity and the Schauder estimates to a class of degenerate parabolic equations of non-divergence form in all dimensions \begin{equation} \mathcal{L}u:= u_t -Lu= u_t -(x a_{11} u_{xx} +2\sqrt{x} \sum_{j=2}^n a_{1j} u_{x y_j} + \sum_{i,j=2}^n a_{ij} u_{y_i y_j} + b_1 u_x +\sum_{j=2}^n b_j u_{y_j} ) =g\ \end{equation} on \(x \geq 0, y=(y_2,\ldots, y_n) \in \mathbb{R}^{n-1}\), with bounded measurable coefficients. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_00675 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hölder regularity of solutions of degenerate parabolic equations of general dimension Jang, Hyo Seok Lee, Ki-Ahm Analysis of PDEs Differential Geometry 35B65, 35K65 We establish the Alexandroff-Bakelman-Pucci estimate, the Harnack inequality, the Hölder regularity and the Schauder estimates to a class of degenerate parabolic equations of non-divergence form in all dimensions \begin{equation} \mathcal{L}u:= u_t -Lu= u_t -(x a_{11} u_{xx} +2\sqrt{x} \sum_{j=2}^n a_{1j} u_{x y_j} + \sum_{i,j=2}^n a_{ij} u_{y_i y_j} + b_1 u_x +\sum_{j=2}^n b_j u_{y_j} ) =g\ \end{equation} on \(x \geq 0, y=(y_2,\ldots, y_n) \in \mathbb{R}^{n-1}\), with bounded measurable coefficients. |
| title | Hölder regularity of solutions of degenerate parabolic equations of general dimension |
| topic | Analysis of PDEs Differential Geometry 35B65, 35K65 |
| url | https://arxiv.org/abs/2412.00675 |