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arXiv · 2502.12287

Boundary Reconstruction for the Anisotropic Fractional Calder\'on Problem

Xiaopeng Cheng·Angkana Rüland
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Abstract

In this article, we provide a boundary reconstruction result for the anisotropic fractional Calder\'on problem and its associated degenerate elliptic extension into the upper half plane. More precisely, considering the setting from \cite{FGKU21}, we show that the metric on the measurement set can be reconstructed from the source-to-solution data. To this end, we rely on the approach by Brown \cite{B01} in the framework developed in \cite{NT01} (see also \cite{KY02}) after localizing the problem by considering it through an extension perspective.

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Xiaopeng Cheng, Angkana Rüland. 2025-02-17. Boundary Reconstruction for the Anisotropic Fractional Calder\'on Problem. https://arxiv.org/abs/2502.12287

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