Stability estimates for an inverse Steklov problem in a class of hollow spheres

Article type: Research Article

Authors: Gendron, Germain^{; *}

Affiliations: Laboratoire de Mathématiques Jean Leray, UMR CNRS 6629, 2 Rue de la Houssinière BP 92208, F-44322 Nantes Cedex 03, France. E-mail: germain.gendron@univ-nantes.fr

Correspondence: [*] Corresponding author. E-mail: germain.gendron@univ-nantes.fr.

Abstract: In this paper, we study an inverse Steklov problem in a class of n-dimensional manifolds having the topology of a hollow sphere and equipped with a warped product metric. Precisely, we aim at studying the continuous dependence of the warping function defining the warped product with respect to the Steklov spectrum. We first show that the knowledge of the Steklov spectrum up to an exponential decreasing error is enough to determine uniquely the warping function in a neighbourhood of the boundary. Second, when the warping functions are symmetric with respect to 1/2, we prove a log-type stability estimate in the inverse Steklov problem. As a last result, we prove a log-type stability estimate for the corresponding Calderón problem.

Keywords: Inverse Calderón problem, Steklov spectrum, Weyl–Titchmarsh functions, Nevanlinna theorem, Müntz–Jackson’s theorem

DOI: 10.3233/ASY-211684

Journal: Asymptotic Analysis, vol. 126, no. 3-4, pp. 323-377, 2022