Schauder type estimates for degenerate or singular elliptic equations with DMO coefficients
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866913573883609088 |
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| author | Dong, Hongjie Jeon, Seongmin Vita, Stefano |
| author_facet | Dong, Hongjie Jeon, Seongmin Vita, Stefano |
| contents | In this paper, we study degenerate or singular elliptic equations in divergence form $$-\text{div}(x_n^αA\nabla u)=\text{div}(x_n^α\mathbf{g})\quad\text{in }B_1\cap\{x_n>0\}.$$ When $α>-1$, we establish boundary Schauder type estimates under the conormal boundary condition on the flat boundary, provided that the coefficients satisfy Dini mean oscillation (DMO) type conditions. Additionally, as an application, we derive higher-order boundary Harnack principles for uniformly elliptic equations in divergence form with DMO coefficients. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2311_06846 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Schauder type estimates for degenerate or singular elliptic equations with DMO coefficients Dong, Hongjie Jeon, Seongmin Vita, Stefano Analysis of PDEs 35B45, 35B65, 35J70, 35J75 In this paper, we study degenerate or singular elliptic equations in divergence form $$-\text{div}(x_n^αA\nabla u)=\text{div}(x_n^α\mathbf{g})\quad\text{in }B_1\cap\{x_n>0\}.$$ When $α>-1$, we establish boundary Schauder type estimates under the conormal boundary condition on the flat boundary, provided that the coefficients satisfy Dini mean oscillation (DMO) type conditions. Additionally, as an application, we derive higher-order boundary Harnack principles for uniformly elliptic equations in divergence form with DMO coefficients. |
| title | Schauder type estimates for degenerate or singular elliptic equations with DMO coefficients |
| topic | Analysis of PDEs 35B45, 35B65, 35J70, 35J75 |
| url | https://arxiv.org/abs/2311.06846 |