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

Germain Gendron (1)

1 LMJL - Laboratoire de Mathématiques Jean Leray

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 dening 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.

Mots clés: Weyl-Titchmarsh functions; Nevan- linna theorem; Inverse Calderón problem; Müntz-Jackson's theorem; Steklov spectrum

Domaines: Théorie spectrale [math.SP]; Equations aux dérivées partielles [math.AP]; Variables complexes [math.CV]; Analyse fonctionnelle [math.FA]

Germain Gendron. Stability estimates for an inverse Steklov problem in a class of hollow spheres. 2020. ⟨hal-02618634⟩