Resonances and balls in obstacle scattering with Neumann boundary conditions

DOI10.3934/IPI.2008.2.335zbMATH Open1180.35400arXiv0801.0660OpenAlexW2078855797MaRDI QIDQ953796

T. J. Christiansen

Publication date: 6 November 2008

Published in: Inverse Problems and Imaging (Search for Journal in Brave)

Abstract: We consider scattering by an obstacle in $Rea{l}^d$, $dgeq3$ odd. We show that for the Neumann Laplacian if an obstacle has the same resonances as the ball of radius $ho$ does, then the obstacle is a ball of radius $ho$. We give related results for obstacles which are disjoint unions of several balls of the same radius.

Full work available at URL: https://arxiv.org/abs/0801.0660

zbMATH Keywords

inverse problemsresonances

Mathematics Subject Classification ID

Scattering theory for PDEs (35P25) Inverse scattering problems in quantum theory (81U40) Scattering theory of linear operators (47A40)

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