The transmission problem with imperfect interfaces of small resistance
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866917442905702400 |
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| author | Fukushima, Shota Ji, Yong-Gwan Kang, Hyeonbae |
| author_facet | Fukushima, Shota Ji, Yong-Gwan Kang, Hyeonbae |
| contents | We consider the transmission problem in presence of interfaces with imperfect bonding. The imperfect bonding condition is characterized by the positive resistance along the interface, which causes discontinuity of the potential across the interface while the flux is continuous. If the interface resistance is zero, then the interface is of perfect bonding, where both the potential and the flux of the solution are continuous across the interface. In this paper, we first construct using layer potentials the solution to the transmission problem with imperfect interfaces. We then prove that the solutions converge in various Sobolev spaces to the solution to the transmission problem with perfect interfaces as the interface resistance tends to zero. In particular, it is shown that the gradient of the solution converges in the uniform norm if the boundary is sufficiently regular. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_25232 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The transmission problem with imperfect interfaces of small resistance Fukushima, Shota Ji, Yong-Gwan Kang, Hyeonbae Analysis of PDEs Primary 35J47, Secondary 31A10, 31B10, 74K15 We consider the transmission problem in presence of interfaces with imperfect bonding. The imperfect bonding condition is characterized by the positive resistance along the interface, which causes discontinuity of the potential across the interface while the flux is continuous. If the interface resistance is zero, then the interface is of perfect bonding, where both the potential and the flux of the solution are continuous across the interface. In this paper, we first construct using layer potentials the solution to the transmission problem with imperfect interfaces. We then prove that the solutions converge in various Sobolev spaces to the solution to the transmission problem with perfect interfaces as the interface resistance tends to zero. In particular, it is shown that the gradient of the solution converges in the uniform norm if the boundary is sufficiently regular. |
| title | The transmission problem with imperfect interfaces of small resistance |
| topic | Analysis of PDEs Primary 35J47, Secondary 31A10, 31B10, 74K15 |
| url | https://arxiv.org/abs/2604.25232 |