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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2408.01073 |
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| _version_ | 1866929446712246272 |
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| author | Jingqi, Liang Lihe, Wang Chunqin, Zhou |
| author_facet | Jingqi, Liang Lihe, Wang Chunqin, Zhou |
| contents | In this paper, we prove the boundary pointwise $C^{0}$-regularity of weak solutions for Dirichlet problem of elliptic equations in divergence form with distributional coefficients, where the boundary value equals to zero. This is a generalization of the interior case. If $Ω$ satisfies some measure condition at one boundary point, the bilinear mapping $\langle V\cdot,\cdot\rangle$ generalized by distributional coefficient $V$ can be controlled by a constant sufficiently small, the nonhomogeneous terms satisfy some Dini decay conditions, then the solution is continuous at this point in the $L^{2}$ sense. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_01073 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Boundary C^α-regularity for solutions of elliptic equations with distributional coefficients Jingqi, Liang Lihe, Wang Chunqin, Zhou Analysis of PDEs In this paper, we prove the boundary pointwise $C^{0}$-regularity of weak solutions for Dirichlet problem of elliptic equations in divergence form with distributional coefficients, where the boundary value equals to zero. This is a generalization of the interior case. If $Ω$ satisfies some measure condition at one boundary point, the bilinear mapping $\langle V\cdot,\cdot\rangle$ generalized by distributional coefficient $V$ can be controlled by a constant sufficiently small, the nonhomogeneous terms satisfy some Dini decay conditions, then the solution is continuous at this point in the $L^{2}$ sense. |
| title | Boundary C^α-regularity for solutions of elliptic equations with distributional coefficients |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2408.01073 |