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| Main Authors: | , |
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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2510.02242 |
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| _version_ | 1866915530911252480 |
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| author | Baers, Hendrik Rüland, Angkana |
| author_facet | Baers, Hendrik Rüland, Angkana |
| contents | We discuss two spectral fractional anisotropic Calderón problems with source-to-solution measurements and their quantitative relation to the classical Calderón problem. Firstly, we consider the anistropic fractional Calderón problem from [FGKU25]. In this setting, we quantify the relation between the local and nonlocal Calderón problems which had been deduced in [R25] and provide an associated stability estimate. As a consequence, any stability result which holds on the level of the local problem with source-to-solution data has a direct nonlocal analogue (up to a logarithmic loss). Secondly, we introduce and discuss the fractional Calderón problem with source-to-solution measurements for the spectral fractional Dirichlet Laplacian on open, bounded, connected, Lipschitz sets on $\mathbb{R}^n$. Also in this context, we provide a qualitative and quantitative transfer of uniqueness from the local to the nonlocal setting. As a consequence, we infer the first stability results for the principal part for a fractional Calderón type problem for which no reduction of Liouville type is known. Our arguments rely on quantitative unique continuation arguments. As a result of independent interest, we also prove a quantitative relation between source-to-solution and Dirichlet-to-Neumann measurements for the classical Calderón problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_02242 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Transfer of Stability from the Classical to the Fractional Anisotropic Calderón Problem Baers, Hendrik Rüland, Angkana Analysis of PDEs We discuss two spectral fractional anisotropic Calderón problems with source-to-solution measurements and their quantitative relation to the classical Calderón problem. Firstly, we consider the anistropic fractional Calderón problem from [FGKU25]. In this setting, we quantify the relation between the local and nonlocal Calderón problems which had been deduced in [R25] and provide an associated stability estimate. As a consequence, any stability result which holds on the level of the local problem with source-to-solution data has a direct nonlocal analogue (up to a logarithmic loss). Secondly, we introduce and discuss the fractional Calderón problem with source-to-solution measurements for the spectral fractional Dirichlet Laplacian on open, bounded, connected, Lipschitz sets on $\mathbb{R}^n$. Also in this context, we provide a qualitative and quantitative transfer of uniqueness from the local to the nonlocal setting. As a consequence, we infer the first stability results for the principal part for a fractional Calderón type problem for which no reduction of Liouville type is known. Our arguments rely on quantitative unique continuation arguments. As a result of independent interest, we also prove a quantitative relation between source-to-solution and Dirichlet-to-Neumann measurements for the classical Calderón problem. |
| title | Transfer of Stability from the Classical to the Fractional Anisotropic Calderón Problem |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2510.02242 |