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2022 Reconstruction and stability in Gelfand’s inverse interior spectral problem
Roberta Bosi, Yaroslav Kurylev, Matti Lassas
Anal. PDE 15(2): 273-326 (2022). DOI: 10.2140/apde.2022.15.273

Abstract

Assume that M is a compact Riemannian manifold of bounded geometry given by restrictions on its diameter, Ricci curvature and injectivity radius. Assume we are given, with some error, the first eigenvalues of the Laplacian Δg on M as well as the corresponding eigenfunctions restricted on an open set in M. We then construct a stable approximation to the manifold (M,g). Namely, we construct a metric space and a Riemannian manifold which differ, in a proper sense, just a little from M when the above data are given with a small error. We give an explicit log-log-type stability estimate on how the constructed manifold and the metric on it depend on the errors in the given data. Moreover a similar stability estimate is derived for the Gelfand inverse problem. The proof is based on methods from geometric convergence, a quantitative stability estimate for the unique continuation and a new version of the geometric boundary control method.

Citation

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Roberta Bosi. Yaroslav Kurylev. Matti Lassas. "Reconstruction and stability in Gelfand’s inverse interior spectral problem." Anal. PDE 15 (2) 273 - 326, 2022. https://doi.org/10.2140/apde.2022.15.273

Information

Received: 4 October 2018; Revised: 3 August 2020; Accepted: 6 October 2020; Published: 2022
First available in Project Euclid: 29 April 2022

Digital Object Identifier: 10.2140/apde.2022.15.273

Subjects:
Primary: 35R30 , 58J05

Keywords: inverse spectral problems , Riemannian manifolds

Rights: Copyright © 2022 Mathematical Sciences Publishers

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Vol.15 • No. 2 • 2022
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