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arXiv · 2611.04749

Increasing stability for the inverse potential problem of the fractional Helmholtz equation

Dong Qiu·Xiang Xu·Yue Zhao
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Abstract

This paper is concerned with the inverse potential scattering problem for the three-dimensional fractional Helmholtz equation. For every $0<α<1$, we establish an increasing stability of determining the potential function from multifrequency exterior measurements of the scattered field. The stability consists of a Lipschitz data discrepancy and a logarithmic remainder that decreases when the upper measured wavenumber increases. The key ingredient in the analysis is to construct appropriate geometric optics solutions, which relate the X-ray transform of the potential to the measured fields. As a consequence, the stability is derived by applying analytic continuation. Two-dimensional numerical examples with noisy near-field data illustrate the benefit of enlarging the measured frequency band for three representative fractional orders.

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Dong Qiu, Xiang Xu, Yue Zhao. 2026-11-03. Increasing stability for the inverse potential problem of the fractional Helmholtz equation. https://arxiv.org/abs/2611.04749

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