On the Frechet differentiability of boundary integral operators in the inverse elastic scattering problem

Charalambopoulos, A

dc.contributor.author	Charalambopoulos, A	en
dc.date.accessioned	2014-03-01T01:11:19Z
dc.date.available	2014-03-01T01:11:19Z
dc.date.issued	1995	en
dc.identifier.issn	0266-5611	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/11604
dc.subject.classification	Mathematics, Applied	en
dc.subject.classification	Physics, Mathematical	en
dc.title	On the Frechet differentiability of boundary integral operators in the inverse elastic scattering problem	en
heal.type	journalArticle	en
heal.identifier.primary	10.1088/0266-5611/11/6/002	en
heal.identifier.secondary	http://dx.doi.org/10.1088/0266-5611/11/6/002	en
heal.identifier.secondary	002	en
heal.language	English	en
heal.publicationDate	1995	en
heal.abstract	This paper is concerned with the study of the Frechet differentiability properties of the operator connecting the scattered field with scatterer's surface in the framework of the inverse elastic scattering problem. We adopt the integral equation approach, which transfers the solution of the inverse problem to the solution of a boundary integral equation of the second kind. We study the behaviour of the appeared integral operators and prove that they constitute Frechet differentiable operators. As we show, this result leads to the conclusion that the scattered elastic field is Frechet differentiable with respect to the boundary of the scatterer. Finally we present a characterization of the Frechet derivative of the scattered field as the solution of a direct scattering elastic problem with suitable Dirichlet boundary conditions.	en
heal.publisher	IOP PUBLISHING LTD	en
heal.journalName	Inverse Problems	en
dc.identifier.doi	10.1088/0266-5611/11/6/002	en
dc.identifier.isi	ISI:A1995TL05600002	en
dc.identifier.volume	11	en
dc.identifier.issue	6	en
dc.identifier.spage	1137	en
dc.identifier.epage	1161	en