Stability estimate for the discrete Calderon problem from partial data
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929340543926272 |
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| author | Zhao, Xiaomeng Yuan, Ganghua |
| author_facet | Zhao, Xiaomeng Yuan, Ganghua |
| contents | In this paper, we focus on the analysis of discrete versions of the Calderon problem with partial boundary data in dimension d >= 3. In particular, we establish logarithmic stability estimates for the discrete Calderon problem on an arbitrarily small portion of the boundary under suitable a priori bounds. For this end, we will use CGO solutions and derive a new discrete Carleman estimate and a key unique continuation estimate. Unlike the continuous case, we use a new strategy inspired by [32] to prove the key discrete unique continuation estimate by utilizing the new Carleman estimate with boundary observations for a discrete Laplace operator. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_06920 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stability estimate for the discrete Calderon problem from partial data Zhao, Xiaomeng Yuan, Ganghua Analysis of PDEs 35R30, 35J25, 65N06 In this paper, we focus on the analysis of discrete versions of the Calderon problem with partial boundary data in dimension d >= 3. In particular, we establish logarithmic stability estimates for the discrete Calderon problem on an arbitrarily small portion of the boundary under suitable a priori bounds. For this end, we will use CGO solutions and derive a new discrete Carleman estimate and a key unique continuation estimate. Unlike the continuous case, we use a new strategy inspired by [32] to prove the key discrete unique continuation estimate by utilizing the new Carleman estimate with boundary observations for a discrete Laplace operator. |
| title | Stability estimate for the discrete Calderon problem from partial data |
| topic | Analysis of PDEs 35R30, 35J25, 65N06 |
| url | https://arxiv.org/abs/2405.06920 |