Stable determination of the potential for the Helmholtz equation in the high frequency limit from boundary measurements
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866915738551320576 |
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| author | Choulli, Mourad Takase, Hiroshi |
| author_facet | Choulli, Mourad Takase, Hiroshi |
| contents | We establish a triple logarithmic stability estimate of determining the potential in a Helmholtz equation from a partial Dirichlet-to-Neumann map in the high frequency limit. This estimate is proved under the assumption that the potential is known near the boundary of a domain when the dimension is greater than or equal to $3$. In addition, we show a triple logarithmic stability for an interior impedance problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_10751 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stable determination of the potential for the Helmholtz equation in the high frequency limit from boundary measurements Choulli, Mourad Takase, Hiroshi Analysis of PDEs We establish a triple logarithmic stability estimate of determining the potential in a Helmholtz equation from a partial Dirichlet-to-Neumann map in the high frequency limit. This estimate is proved under the assumption that the potential is known near the boundary of a domain when the dimension is greater than or equal to $3$. In addition, we show a triple logarithmic stability for an interior impedance problem. |
| title | Stable determination of the potential for the Helmholtz equation in the high frequency limit from boundary measurements |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2501.10751 |