The Role of Non-Negative Polynomials For Rank-One Convexity and Quasi Convexity

Detalhes bibliográficos
Autor(a) principal: Bandeira, Luís
Data de Publicação: 2017
Outros Autores: Pedregal, Pablo
Tipo de documento: Artigo
Idioma: por
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10174/21483
https://doi.org/10.1007/BF03377390
Resumo: We stress the relationship between the non-negativeness of polynomials and quasi convexity and rank-one convexity. In particular, we translate the celebrated theorem of Hilbert ([3]) about non-negativeness of polynomials and sums of squares, into a test for rank-one convex functions defined on 2 × 2-matrices. Even if the density for an integral functional is a fourth-degree, homogeneous polynomial, quasi convexity cannot be reduced to the non-negativeness of polynomials of a fixed, finite number of variables.
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spelling The Role of Non-Negative Polynomials For Rank-One Convexity and Quasi ConvexityRank-one convexityquasi convexitynon-negative polynomialsWe stress the relationship between the non-negativeness of polynomials and quasi convexity and rank-one convexity. In particular, we translate the celebrated theorem of Hilbert ([3]) about non-negativeness of polynomials and sums of squares, into a test for rank-one convex functions defined on 2 × 2-matrices. Even if the density for an integral functional is a fourth-degree, homogeneous polynomial, quasi convexity cannot be reduced to the non-negativeness of polynomials of a fixed, finite number of variables.Springer2017-11-28T12:20:31Z2017-11-282017-01-09T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://hdl.handle.net/10174/21483https://doi.org/10.1007/BF03377390http://hdl.handle.net/10174/21483https://doi.org/10.1007/BF03377390porBandeira, L. & Pedregal, P. J Elliptic Parabol Equ (2016) 2: 27.lmzb@uevora.ptpablo.pedregal@uclm.es334Bandeira, LuísPedregal, Pabloinfo:eu-repo/semantics/embargoedAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-01-03T19:12:02Zoai:dspace.uevora.pt:10174/21483Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T01:12:42.689836Repositório 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 The Role of Non-Negative Polynomials For Rank-One Convexity and Quasi Convexity
title The Role of Non-Negative Polynomials For Rank-One Convexity and Quasi Convexity
spellingShingle The Role of Non-Negative Polynomials For Rank-One Convexity and Quasi Convexity
Bandeira, Luís
Rank-one convexity
quasi convexity
non-negative polynomials
title_short The Role of Non-Negative Polynomials For Rank-One Convexity and Quasi Convexity
title_full The Role of Non-Negative Polynomials For Rank-One Convexity and Quasi Convexity
title_fullStr The Role of Non-Negative Polynomials For Rank-One Convexity and Quasi Convexity
title_full_unstemmed The Role of Non-Negative Polynomials For Rank-One Convexity and Quasi Convexity
title_sort The Role of Non-Negative Polynomials For Rank-One Convexity and Quasi Convexity
author Bandeira, Luís
author_facet Bandeira, Luís
Pedregal, Pablo
author_role author
author2 Pedregal, Pablo
author2_role author
dc.contributor.author.fl_str_mv Bandeira, Luís
Pedregal, Pablo
dc.subject.por.fl_str_mv Rank-one convexity
quasi convexity
non-negative polynomials
topic Rank-one convexity
quasi convexity
non-negative polynomials
description We stress the relationship between the non-negativeness of polynomials and quasi convexity and rank-one convexity. In particular, we translate the celebrated theorem of Hilbert ([3]) about non-negativeness of polynomials and sums of squares, into a test for rank-one convex functions defined on 2 × 2-matrices. Even if the density for an integral functional is a fourth-degree, homogeneous polynomial, quasi convexity cannot be reduced to the non-negativeness of polynomials of a fixed, finite number of variables.
publishDate 2017
dc.date.none.fl_str_mv 2017-11-28T12:20:31Z
2017-11-28
2017-01-09T00:00:00Z
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/10174/21483
https://doi.org/10.1007/BF03377390
http://hdl.handle.net/10174/21483
https://doi.org/10.1007/BF03377390
url http://hdl.handle.net/10174/21483
https://doi.org/10.1007/BF03377390
dc.language.iso.fl_str_mv por
language por
dc.relation.none.fl_str_mv Bandeira, L. & Pedregal, P. J Elliptic Parabol Equ (2016) 2: 27.
lmzb@uevora.pt
pablo.pedregal@uclm.es
334
dc.rights.driver.fl_str_mv info:eu-repo/semantics/embargoedAccess
eu_rights_str_mv embargoedAccess
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)
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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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