An inverse boundary value problem in electrodynamics
type: Item
instance of: scholarly article
title: An inverse boundary value problem in electrodynamics
zbMATH Open document ID: 0804.35152
DOI: 10.1215/S0012-7094-93-07014-7
author: Petri Ola
author: Lassi Päivärinta
author: Erkki Somersalo
published in: Duke Mathematical Journal
publication date: 1995-01-15T00:00:00Z
review text: Let \(\Omega\) be a bounded domain in \(\mathbb{R}^ 3\) with a smooth boundary \(\Gamma\) and a connected complement. Let the electric permittivity, conductivity and magnetic permeability be denoted by \(\varepsilon\), \(\sigma\) and \(\mu\) respectively. Let \(E\), \(H\) denote respectively the electric and magnetic fields inside \(\Omega\). Suppose the map \(\Lambda\) that assigns the tangential component of \(E_ \Gamma\) to that of \(H_ \Gamma\) is defined. Assume that outside \(\Omega\), \(\varepsilon\), \(\mu\) are known constants and \(\sigma\) vanishes. Then, it is proved that, under appropriate smoothness and boundedness conditions on \(\varepsilon\), \(\sigma\) and \(\mu\), the knowledge of the map \(\Lambda\) uniquely determines these quantities.
reviewed by: Dang Dinh Ang
Mathematics Subject Classification ID: 35R30
Mathematics Subject Classification ID: 35Q60
Mathematics Subject Classification ID: 78A25
zbMATH DE Number: 558978
zbMATH Keywords: unique determination of electric permittivity, conductivity, magnetic permeability
MaRDI profile type: Publication
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full work available at URL: s0012-7094-93-07014-7
OpenAlex ID: W2048309834
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description: scientific article; zbMATH DE number 558978