Stable determination of unbounded potential by asymptotic boundary spectral data

Yavar Kian; Éric Soccorsi

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arXiv · 2203.09757

Stable determination of unbounded potential by asymptotic boundary spectral data

Yavar Kian·Éric Soccorsi

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Abstract

We consider the Dirichlet Laplacian $A_q=-\Delta+q$ in a bounded domain $\Omega \subset \mathbb{R}^d$, $d \ge 3$, with real-valued perturbation $q \in L^{\max(2 , 3 d / 5)}(\Omega)$. We examine the stability issue in the inverse problem of determining the electric potential $q$ from the asymptotic behavior of the eigenvalues of $A_q$. Assuming that the boundary measurement of the normal derivative of the eigenfunctions is a square summable sequence in $L^2(\partial \Omega)$, we prove that $q$ can be H\"older stably retrieved through knowledge of the asymptotics of the eigenvalues

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Yavar Kian, Éric Soccorsi. 2022-03-18. Stable determination of unbounded potential by asymptotic boundary spectral data. https://arxiv.org/abs/2203.09757

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