Well-posedness of domain integral equations for a dielectric object in homogeneous background
type: Item
instance of: scholarly article
title: Well-posedness of domain integral equations for a dielectric object in homogeneous background
zbMATH Open document ID: 1158.78003
author: M. C. van Beurden
author: Stephanus J. L. Van Eijndhoven
published in: Journal of Engineering Mathematics
publication date: 2009-02-11T00:00:00Z
review text: This paper deals with various properties of a dielectric object. There are analyzed the integro-differential equations for the contrast current density, for the electric field and for the generalized electric-flux density and it is established the existence of bounded inverses with respect to various function spaces. The authors show that these equations can be reduced to a Fredholm integral equation of the second kind with a unique solution. It is also argued that the problems are well-posed with respect to three different function spaces and that the conditions for the well-posedness of the equations are identical. The proofs strongly rely on the Riesz-Fredholm theory, combined with the Helmholtz decomposition and the Sobolev embedding theorem.
reviewed by: Teodora-Liliana Rădulescu
Mathematics Subject Classification ID: 78A25
Mathematics Subject Classification ID: 45B05
Mathematics Subject Classification ID: 46N20
Mathematics Subject Classification ID: 49K40
zbMATH DE Number: 5506384
zbMATH Keywords: dielectric objects
zbMATH Keywords: electromagnetic scattering
zbMATH Keywords: integral equations
zbMATH Keywords: well-posedness
MaRDI profile type: Publication
full work available at URL: s10665-008-9218-2
OpenAlex ID: W2161070589
cites work: Q5732462
cites work: Q3672341
cites work: Linear integral equations
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cites work: A potential integral equations method for electromagnetic scattering by penetrable bodies
DOI: 10.1007/S10665-008-9218-2
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description: scientific article; zbMATH DE number 5506384