Determination of the Schrödinger-Robin operator by incomplete or asymptotic spectral boundary data

2025/07/09 by Mourad Choulli, Choulli, Mourad, Abdelmalek Metidji +3 · 1 citation
Engineering · Mathematics · #35J10 #35P10 #35R30 #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2507.06598

openalex publication_date 2025/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This article deals with the inverse problem of determining the unbounded real-valued electric potential of the Robin Laplacian on a bounded domain of dimension 3 or greater, by incomplete knowledge of its boundary spectral data. Namely, the main result establishes that the unknown potential can be Hölder stably retrieved from the asymptotic behavior of the eigenvalues and the sequence of the boundary measurements of the corresponding eigenfunctions where finitely many terms are missing.

Citations

• Two parabolic inverse problems for an equation with unbounded zero-order coefficient
• A quantitative Borg-Levinson theorem for a large class of unbounded potentials
• Stable determination of unbounded potential by asymptotic boundary spectral data
• Identification of unbounded electric potentials through asymptotic boundary spectral data
• A Borg-Levinson theorem for magnetic Schr "odinger operators on a\n Riemannian manifold
• Multidimensional Borg--Levinson theorems for unbounded potentials
• Stability for the multi-dimensional Borg-Levinson theorem with partial spectral data
• A Global Uniqueness Theorem for an Inverse Boundary Value Problem

Cited by

• Inverse spectral problems for higher-order coefficients

Related

• Multidimensionnel Borg-Levinson uniqueness and stability results for the Robin Laplacian with unbounded potential
• Stable determination of unbounded potential by asymptotic boundary spectral data
• Identification of unbounded electric potentials through asymptotic boundary spectral data
• Reconstructing the potential for the 1D Schrödinger equation from boundary measurements
• The inverse Robin boundary value problem in a half-space