A variational formulation for Dirac operators in bounded domains: applications to spectral geometric inequalities

Detalhes bibliográficos
Autor(a) principal: Antunes, Pedro R. S.
Data de Publicação: 2021
Outros Autores: Benguria, Rafael, Lotoreichik, Vladimir, Ourmières-Bonafos, Thomas
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10400.2/10710
Resumo: We investigate spectral features of the Dirac operator with infinite mass boundary conditions in a smooth bounded domain of $\mathbb{R}^2$. Motivated by spectral geometric inequalities, we prove a non-linear variational formulation to characterize its principal eigenvalue. This characterization turns out to be very robust and allows for a simple proof of a Szeg\"o type inequality as well as a new reformulation of a Faber-Krahn type inequality for this operator. The paper is complemented with strong numerical evidences supporting the existence of a Faber-Krahn type inequality.
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spelling A variational formulation for Dirac operators in bounded domains: applications to spectral geometric inequalitiesWe investigate spectral features of the Dirac operator with infinite mass boundary conditions in a smooth bounded domain of $\mathbb{R}^2$. Motivated by spectral geometric inequalities, we prove a non-linear variational formulation to characterize its principal eigenvalue. This characterization turns out to be very robust and allows for a simple proof of a Szeg\"o type inequality as well as a new reformulation of a Faber-Krahn type inequality for this operator. The paper is complemented with strong numerical evidences supporting the existence of a Faber-Krahn type inequality.SpringerRepositório AbertoAntunes, Pedro R. S.Benguria, RafaelLotoreichik, VladimirOurmières-Bonafos, Thomas2021-05-07T10:30:34Z20212021-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.2/10710eng0010-3616 (Print)info: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:RCAAP2023-11-16T15:36:39Zoai:repositorioaberto.uab.pt:10400.2/10710Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T22:50:14.936310Repositório 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 A variational formulation for Dirac operators in bounded domains: applications to spectral geometric inequalities
title A variational formulation for Dirac operators in bounded domains: applications to spectral geometric inequalities
spellingShingle A variational formulation for Dirac operators in bounded domains: applications to spectral geometric inequalities
Antunes, Pedro R. S.
title_short A variational formulation for Dirac operators in bounded domains: applications to spectral geometric inequalities
title_full A variational formulation for Dirac operators in bounded domains: applications to spectral geometric inequalities
title_fullStr A variational formulation for Dirac operators in bounded domains: applications to spectral geometric inequalities
title_full_unstemmed A variational formulation for Dirac operators in bounded domains: applications to spectral geometric inequalities
title_sort A variational formulation for Dirac operators in bounded domains: applications to spectral geometric inequalities
author Antunes, Pedro R. S.
author_facet Antunes, Pedro R. S.
Benguria, Rafael
Lotoreichik, Vladimir
Ourmières-Bonafos, Thomas
author_role author
author2 Benguria, Rafael
Lotoreichik, Vladimir
Ourmières-Bonafos, Thomas
author2_role author
author
author
dc.contributor.none.fl_str_mv Repositório Aberto
dc.contributor.author.fl_str_mv Antunes, Pedro R. S.
Benguria, Rafael
Lotoreichik, Vladimir
Ourmières-Bonafos, Thomas
description We investigate spectral features of the Dirac operator with infinite mass boundary conditions in a smooth bounded domain of $\mathbb{R}^2$. Motivated by spectral geometric inequalities, we prove a non-linear variational formulation to characterize its principal eigenvalue. This characterization turns out to be very robust and allows for a simple proof of a Szeg\"o type inequality as well as a new reformulation of a Faber-Krahn type inequality for this operator. The paper is complemented with strong numerical evidences supporting the existence of a Faber-Krahn type inequality.
publishDate 2021
dc.date.none.fl_str_mv 2021-05-07T10:30:34Z
2021
2021-01-01T00:00:00Z
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/10400.2/10710
url http://hdl.handle.net/10400.2/10710
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0010-3616 (Print)
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 Springer
publisher.none.fl_str_mv Springer
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
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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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