New results on transmission eigenvalues

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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 http://hdl.handle.net/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.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

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