Boundary Reconstruction for the Anisotropic Fractional Calderón Problem

2025/02/17 by Cheng, Xiaopeng, Rüland, Angkana · 2 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2502.12287

Abstract

In this article, we provide a boundary reconstruction result for the anisotropic fractional Calderón problem and its associated degenerate elliptic extension into the upper half plane. More precisely, considering the setting from \citeFGKU21, 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 \citeB01 in the framework developed in \citeNT01 (see also \citeKY02) after localizing the problem by considering it through an extension perspective.

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• The higher-order fractional Schrödinger equation with nonlinear local perturbations: Uniqueness
• Anisotropic Calderón problem of a nearly Laplace-Beltrami operator of order 2+

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