2018/07/23 by Mourad Bellassoued, Mourad Choulli, Bellassoued, Mourad +7 · 3 citations
Computer Science · Mathematics · #35J10 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Primary 35R30 #Secondary: 35P99 #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1807.08857
openalex publication_date 2018/07/23 · openalex created_date 2022/08/04 · openalex updated_date 2026/07/28
This article is concerned with uniqueness and stability issues for the\ninverse spectral problem of recovering the magnetic field and the electric\npotential in a Riemannian manifold from some asymptotic knowledge of the\nboundary spectral data of the corresponding Schr "odinger operator under\nDirichlet boundary conditions. The spectral data consist of some asymptotic\nknowledge of a subset of eigenvalues and Neumann traces of the associated\neigenfunctions of the magnetic Laplacian. We also address the same question for\nSchr "odinger operators under Neumann boundary conditions, in which case we\nmeasure the Dirichlet traces of eigenfunctions. In our results we characterize\nthe uniqueness of the magnetic field from a rate of growth of the eigenvalues,\ncombined with suitable asymptotic properties of boundary observation of\neigenfunctions, of the associated magnetic Schr "odinger operator. To our best\nknowledge this is the first result proving uniqueness from such general\nasymptotic behavior of boundary spectral data.\n