Resonances and balls in obstacle scattering with Neumann boundary conditions
type: Item
instance of: scholarly article
title: Resonances and balls in obstacle scattering with Neumann boundary conditions
zbMATH Open document ID: 1180.35400
published in: Inverse Problems and Imaging
publication date: 2008-11-06T00:00:00Z
full work available at URL: https://arxiv.org/abs/0801.0660
review text: The goal of this note is to show that for obstacle scattering in \(\mathbb{R}^N\), \(N\geq 3\) odd, a ball is uniquely determined by its resonance for the Laplacian with Neumann boundary conditions. The author actually shows a somewhat stronger result: If \({\mathcal O}_1\) and \({\mathcal O}_2\) have the same (Neumann) resonances and \({\mathcal O}_1\) is the disjoint union of \(m\) balls, each of radius \(\rho\), then so is \({\mathcal O}_2\).
reviewed by: Messoud Efendiev
Mathematics Subject Classification ID: 35P25
Mathematics Subject Classification ID: 47A40
Mathematics Subject Classification ID: 81U40
zbMATH DE Number: 5362900
zbMATH Keywords: resonances
zbMATH Keywords: inverse problems
author: T. J. Christiansen
MaRDI profile type: Publication
OpenAlex ID: W2078855797
arXiv ID: 0801.0660
DOI: 10.3934/IPI.2008.2.335
description: scientific article