Yaroslav Kurylev et al 2005 Inverse Problems 21 1685 doi:10.1088/0266-5611/21/5/011
Yaroslav Kurylev1, Matti Lassas2 and Ricardo Weder3
Show affiliationsWe consider the inverse problem of the reconstruction of a Schrödinger operator on an unknown Riemannian manifold or a domain of Euclidean space. The data used are a part of the boundary Σ and the eigenvalues corresponding to a set of impedances in the Robin boundary condition which vary on Σ. The proof is based on the analysis of the behaviour of the eigenfunctions on the boundary as well as the perturbation theory of eigenvalues. These reduces the problem to an inverse boundary spectral problem solved by the boundary control method.
58J60 Relations with special manifold structures (Riemannian, Finsler, etc.)
35J10 Schrödinger operator (See also 35Pxx)
35R30 Inverse problems (undetermined coefficients, etc.) for PDE
Issue 5 (October 2005)
Received 24 March 2005, in final form 11 August 2005
Published 16 September 2005
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