Mixed type boundary value problem of elliptic equation in a thin domain
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916311867588608 |
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| author | Hu, Dian Huang, Genggeng |
| author_facet | Hu, Dian Huang, Genggeng |
| contents | In this paper, we prove the a priori estimates for two-dimensional second order homogeneous linear elliptic equations in a narrow region. In a crescent-shaped area, part of the boundary is subject to an oblique derivative boundary condition, while the other part of the boundary is subject to a Dirichlet boundary condition. We show that, as the crescent-shaped area collapses into a segment under suitable conditions, the boundary value problem obeys uniform Schauder estimates and induces an asymptotic estimate. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_03592 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Mixed type boundary value problem of elliptic equation in a thin domain Hu, Dian Huang, Genggeng Analysis of PDEs In this paper, we prove the a priori estimates for two-dimensional second order homogeneous linear elliptic equations in a narrow region. In a crescent-shaped area, part of the boundary is subject to an oblique derivative boundary condition, while the other part of the boundary is subject to a Dirichlet boundary condition. We show that, as the crescent-shaped area collapses into a segment under suitable conditions, the boundary value problem obeys uniform Schauder estimates and induces an asymptotic estimate. |
| title | Mixed type boundary value problem of elliptic equation in a thin domain |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2407.03592 |