An inverse eigenvalue problem for an arbitrary multiply connected bounded region: An extension to higher dimensions
type: Item
instance of: scholarly article
title: An inverse eigenvalue problem for an arbitrary multiply connected bounded region: An extension to higher dimensions
zbMATH Open document ID: 0780.35114
DOI: 10.1155/S0161171293000596
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1993-12-09T00:00:00Z
full work available at URL: https://eudml.org/doc/46899
review text: Summary: The basic problem is that of determining the geometry of an arbitrary multiply connected bounded region in \(\mathbb{R}^ 3\) together with the mixed boundary conditions, from the complete knowledge of the eigenvalues \(\{\lambda_ j\}^ \infty_{j=1}\) for the negative Laplacian, using the asymptotic expansion of the spectral function \(\Theta(t)= \sum^ \infty_{j=1} \exp(-t\lambda_ j)\) as \(t\to 0\).
Mathematics Subject Classification ID: 35R30
Mathematics Subject Classification ID: 35P05
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 35K05
zbMATH DE Number: 436729
zbMATH Keywords: domain identification problem
zbMATH Keywords: Green's function
zbMATH Keywords: heat equation
zbMATH Keywords: membrane equation
zbMATH Keywords: inverse problem
zbMATH Keywords: Laplace operator
zbMATH Keywords: asymptotic expansion
zbMATH Keywords: spectral function
author: Elsayed M. E. Zayed
MaRDI profile type: Publication
OpenAlex ID: W2009667469
description: scientific article; zbMATH DE number 436729