Neumann resonances in linear elasticity for an arbitrary body
type: Item
instance of: scholarly article
title: Neumann resonances in linear elasticity for an arbitrary body
zbMATH Open document ID: 0851.35032
DOI: 10.1007/BF02099253
published in: Communications in Mathematical Physics
publication date: 1996-11-18T00:00:00Z
review text: The resonances associated to the Lamé operator \(L\) in the exterior of an arbitrary obstacle in \(\mathbb{R}^3\) with Neumann boundary conditions are analyzed. The resonances are defined as the poles of the meromorphic continuation of the cut-off resolvent from the lower half plane \((\text{Im } y< 0)\) to the whole complex plane \(\mathbb{C}\). The main result of the paper is the following: There exist two infinite sequences \(\{\lambda_j\}\), \(\{\overline \lambda_j\}\) of distinct resonances of the Lamé operator \(L\), such that \(0< \text{Im } \lambda_j\leq C_N|\lambda_j|^{- N}\) for any \(N> 0\).
Mathematics Subject Classification ID: 35J15
Mathematics Subject Classification ID: 74B05
zbMATH DE Number: 906555
zbMATH Keywords: meromorphic continuation of the cut-off resolvent
zbMATH Keywords: resonances of the Lamé operator
author: Plamen Stefanov
author: Georgi Vodev
reviewed by: István Ecsedi
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 906555