Stability and Reconstruction in Gel’fand Inverse Boundary Spectral Problem

Atsushi Katsuda, Yaroslav Kurylev and Matti Lassas
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Atsushi Katsuda: Okayama University, Department of Mathematics
Yaroslav Kurylev: Loughborough University, Department of Mathematical Sciences
Matti Lassas: University of Helsinki, Rolf Nevanlinna Institute

A chapter in New Analytic and Geometric Methods in Inverse Problems, 2004, pp 309-322 from Springer

Abstract: Abstract In this paper we study stability and approximate reconstruction in the inverse boundary spectral problem (the generalized Gelfand inverse problem [12]) for Riemannian manifolds. We denote by (M, g) an unknown, m-dimensional, compact connected Riemannian manifold with a (smooth) metric g and non-empty boundary ∂M. The boundary ∂M is itself an (m − 1)-dimensional compact differentiable manifold. We do not assume the knowledge of i* (g) on ∂M, where i : ∂M → M is an embedding or the corresponding area element dS g . Because the boundary ∂M is known, we will consider a class M = M ∂M of compact, connected Riemannian manifolds which have the same boundary, ∂M.

Keywords: Inverse Problem; Riemannian Manifold; Unique Continuation; Boundary Distance; Carleman Estimate (search for similar items in EconPapers)
Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-662-08966-8_10

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DOI: 10.1007/978-3-662-08966-8_10

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