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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.10923 |
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| _version_ | 1866909761776123904 |
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| author | Wu, Weijia Hu, Yaozhong Yang, Donghui Zhong, Jie |
| author_facet | Wu, Weijia Hu, Yaozhong Yang, Donghui Zhong, Jie |
| contents | This paper investigates the quantitative weak unique continuation property (QWUCP) for a class of high-dimensional elliptic equations with interior point degeneracy. First, we establish well-posedness results in weighted function spaces. Then, using an innovative approximation method, we derive the three-ball theorem at the degenerate point. Finally, we apply the three-ball theorem to prove QWUCP for two different cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_10923 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Approximation of Elliptic Equations with Interior Single-Point Degeneracy and Its Application to Weak Unique Continuation Property Wu, Weijia Hu, Yaozhong Yang, Donghui Zhong, Jie Analysis of PDEs This paper investigates the quantitative weak unique continuation property (QWUCP) for a class of high-dimensional elliptic equations with interior point degeneracy. First, we establish well-posedness results in weighted function spaces. Then, using an innovative approximation method, we derive the three-ball theorem at the degenerate point. Finally, we apply the three-ball theorem to prove QWUCP for two different cases. |
| title | Approximation of Elliptic Equations with Interior Single-Point Degeneracy and Its Application to Weak Unique Continuation Property |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2501.10923 |