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| Main Author: | |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2307.12466 |
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| _version_ | 1866915961446072320 |
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| author | Zhang, Chilin |
| author_facet | Zhang, Chilin |
| contents | We prove the $C^{2,α}$ regularity of the free boundary in the Signorini problem with variable coefficients. We use a $C^{1,α}$ boundary Harnack inequality in slit domain. The key method is to study a non-standard degenerate elliptic equation and obtain a $C^{1,α}$ Schauder estimate. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_12466 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The $C^{1,α}$ boundary Harnack principle in a slit domain and its application to the Signorini problem Zhang, Chilin Analysis of PDEs We prove the $C^{2,α}$ regularity of the free boundary in the Signorini problem with variable coefficients. We use a $C^{1,α}$ boundary Harnack inequality in slit domain. The key method is to study a non-standard degenerate elliptic equation and obtain a $C^{1,α}$ Schauder estimate. |
| title | The $C^{1,α}$ boundary Harnack principle in a slit domain and its application to the Signorini problem |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2307.12466 |