Partial data stability for the inverse fractional conductivity problem
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908378652999680 |
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| author | Covi, Giovanni Kujanpää, Antti Railo, Jesse |
| author_facet | Covi, Giovanni Kujanpää, Antti Railo, Jesse |
| contents | The classical Calderón problem with partial data is known to be log-log stable in some special cases, but even the uniqueness problem is open in general. We study the partial data stability of an analogous inverse fractional conductivity problem on bounded smooth domains. Using the fractional Liouville reduction, we obtain a log-log stability estimate when the conductivities a priori agree in the measurement set and their difference has compact support. In the case in which the conductivities are assumed to agree a priori in the whole exterior of the domain, we obtain a shaper logarithmic stability estimate. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_18567 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Partial data stability for the inverse fractional conductivity problem Covi, Giovanni Kujanpää, Antti Railo, Jesse Analysis of PDEs 35R30 (Primary) 26A33, 42B37 (Secondary) The classical Calderón problem with partial data is known to be log-log stable in some special cases, but even the uniqueness problem is open in general. We study the partial data stability of an analogous inverse fractional conductivity problem on bounded smooth domains. Using the fractional Liouville reduction, we obtain a log-log stability estimate when the conductivities a priori agree in the measurement set and their difference has compact support. In the case in which the conductivities are assumed to agree a priori in the whole exterior of the domain, we obtain a shaper logarithmic stability estimate. |
| title | Partial data stability for the inverse fractional conductivity problem |
| topic | Analysis of PDEs 35R30 (Primary) 26A33, 42B37 (Secondary) |
| url | https://arxiv.org/abs/2505.18567 |