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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 Hölder stably retrieved through knowledge of the asymptotics of the eigenvalues.

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Stable Determination of Unbounded Potential by Asymptotic Boundary Spectral Data

  • 会议论文

  • 发表日期：

    2025年

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  • Yavar Kian,
  • Éric Soccorsi

摘要

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 Hölder stably retrieved through knowledge of the asymptotics of the eigenvalues.