Weyl Type Bound on Positive Interior Transmission Eigenvalues

Detalhes bibliográficos
Autor(a) principal: Lakshtanov, Evgeny
Data de Publicação: 2014
Outros Autores: Vainberg, Boris
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10773/21943
Resumo: This paper contains a lower bound of the Weyl type on the counting function of the positive eigenvalues of the interior transmission eigenvalue problem which justifies the existence of an infinite set of positive interior transmission eigenvalues. We consider the classical transmission problem as well as the case where the inhomogeneous medium contains an obstacle. One of the essential components of the proof is an estimate for the D-t-N operator for the Helmholtz equation for positive λ that replaces the standard parameter-elliptic estimate valid outside of the positive semi-axis.
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spelling Weyl Type Bound on Positive Interior Transmission EigenvaluesCounting functionInterior transmission eigenvaluesWeyl formulaThis paper contains a lower bound of the Weyl type on the counting function of the positive eigenvalues of the interior transmission eigenvalue problem which justifies the existence of an infinite set of positive interior transmission eigenvalues. We consider the classical transmission problem as well as the case where the inhomogeneous medium contains an obstacle. One of the essential components of the proof is an estimate for the D-t-N operator for the Helmholtz equation for positive λ that replaces the standard parameter-elliptic estimate valid outside of the positive semi-axis.Taylor & Francis2018-01-30T16:49:23Z2014-04-01T00:00:00Z2014-04info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/21943eng0036-141010.1080/03605302.2014.881853Lakshtanov, EvgenyVainberg, Borisinfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-02-22T11:42:42Zoai:ria.ua.pt:10773/21943Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T02:56:07.837265Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv Weyl Type Bound on Positive Interior Transmission Eigenvalues
title Weyl Type Bound on Positive Interior Transmission Eigenvalues
spellingShingle Weyl Type Bound on Positive Interior Transmission Eigenvalues
Lakshtanov, Evgeny
Counting function
Interior transmission eigenvalues
Weyl formula
title_short Weyl Type Bound on Positive Interior Transmission Eigenvalues
title_full Weyl Type Bound on Positive Interior Transmission Eigenvalues
title_fullStr Weyl Type Bound on Positive Interior Transmission Eigenvalues
title_full_unstemmed Weyl Type Bound on Positive Interior Transmission Eigenvalues
title_sort Weyl Type Bound on Positive Interior Transmission Eigenvalues
author Lakshtanov, Evgeny
author_facet Lakshtanov, Evgeny
Vainberg, Boris
author_role author
author2 Vainberg, Boris
author2_role author
dc.contributor.author.fl_str_mv Lakshtanov, Evgeny
Vainberg, Boris
dc.subject.por.fl_str_mv Counting function
Interior transmission eigenvalues
Weyl formula
topic Counting function
Interior transmission eigenvalues
Weyl formula
description This paper contains a lower bound of the Weyl type on the counting function of the positive eigenvalues of the interior transmission eigenvalue problem which justifies the existence of an infinite set of positive interior transmission eigenvalues. We consider the classical transmission problem as well as the case where the inhomogeneous medium contains an obstacle. One of the essential components of the proof is an estimate for the D-t-N operator for the Helmholtz equation for positive λ that replaces the standard parameter-elliptic estimate valid outside of the positive semi-axis.
publishDate 2014
dc.date.none.fl_str_mv 2014-04-01T00:00:00Z
2014-04
2018-01-30T16:49:23Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10773/21943
url http://hdl.handle.net/10773/21943
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0036-1410
10.1080/03605302.2014.881853
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Taylor & Francis
publisher.none.fl_str_mv Taylor & Francis
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron:RCAAP
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str RCAAP
institution RCAAP
reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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