Uniqueness results in the inverse spectral Steklov problem

Germain Gendron

doi:10.3934/ipi.2020029

Article Contents

2020, Volume 14, Issue 4: 631-664. Doi: 10.3934/ipi.2020029

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Uniqueness results in the inverse spectral Steklov problem

Germain Gendron^,

Laboratoire de Mathématiques Jean Leray, UMR CNRS 6629, 2 Rue de la Houssinière BP 92208, F-44322 Nantes Cedex 03, France

Received: June 2019

Revised: January 2020

Published online: May 6, 2020

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Abstract

This paper is devoted to an inverse Steklov problem for a particular class of $ n $-dimensional manifolds having the topology of a hollow sphere and equipped with a warped product metric. We prove that the knowledge of the Steklov spectrum determines uniquely the associated warping function up to a natural invariance.

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Mathematics Subject Classification: Primary: 58J53, 35P20; Secondary: 30D35.

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References

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