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arXiv · 2510.02242

Transfer of Stability from the Classical to the Fractional Anisotropic Calderón Problem

Hendrik Baers·Angkana Rüland
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Abstract

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.

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Hendrik Baers, Angkana Rüland. 2025-10-02. Transfer of Stability from the Classical to the Fractional Anisotropic Calderón Problem. https://arxiv.org/abs/2510.02242

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