New results on transmission eigenvalues

Cakoni, F; Gintides, D

dc.contributor.author	Cakoni, F	en
dc.contributor.author	Gintides, D	en
dc.date.accessioned	2014-03-01T01:33:55Z
dc.date.available	2014-03-01T01:33:55Z
dc.date.issued	2010	en
dc.identifier.issn	1930-8337	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/20617
dc.subject	Inhomogeneous medium	en
dc.subject	Interior transmission problem	en
dc.subject	Inverse scattering problem	en
dc.subject	Transmission eigenvalues	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.classification	Physics, Mathematical	en
dc.subject.other	INHOMOGENEOUS-MEDIUM	en
dc.subject.other	EXISTENCE	en
dc.subject.other	MEDIA	en
dc.title	New results on transmission eigenvalues	en
heal.type	journalArticle	en
heal.identifier.primary	10.3934/ipi.2010.4.39	en
heal.identifier.secondary	http://dx.doi.org/10.3934/ipi.2010.4.39	en
heal.language	English	en
heal.publicationDate	2010	en
heal.abstract	We consider the interior transmission eigenvalue problem corresponding to the inverse scattering problem for an isotropic inhomogeneous medium. We first prove that transmission eigenvalues exist for media with index of refraction greater or less than one without assuming that the contrast is sufficiently large. Then we show that for an arbitrary Lipshitz domain with constant index of refraction there exists an infinite discrete set of transmission eigenvalues that accumulate at infinity. Finally, for the general case of non constant index of refraction we provide a lower and an upper bound for the first transmission eigenvalue in terms of the first transmission eigenvalue for appropriate balls with constant index of refraction. © 2010 American Institute of Mathematical Sciences.	en
heal.publisher	AMER INST MATHEMATICAL SCIENCES	en
heal.journalName	Inverse Problems and Imaging	en
dc.identifier.doi	10.3934/ipi.2010.4.39	en
dc.identifier.isi	ISI:000276414600004	en
dc.identifier.volume	4	en
dc.identifier.issue	1	en
dc.identifier.spage	39	en
dc.identifier.epage	48	en