Desigualdade de Adams em domínios ilimitados
Autor(a) principal: | |
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Data de Publicação: | 2018 |
Tipo de documento: | Dissertação |
Idioma: | por |
Título da fonte: | Repositório Institucional da UFG |
Texto Completo: | http://repositorio.bc.ufg.br/tede/handle/tede/8859 |
Resumo: | In this work our aim is to present an extension of the Trudinger-Moser inequality [20] in unbounded domains of Rn for Sobolev Spaces involving high order derivatives. This inequality is nowadays known as Adams-type inequality [1]. We study the techniques developed in the works due to F. Sani and B. Ruf in [23] and due to N. Lam and G. Lu in [16] which are, essentially, combinations of the Comparison Principle of Trombetti and Vazquez for polyharmonic operators and a symmetrization argument, also known as Schwarz Symmetrization. "With such techniques in hands", our aim is to reduce our problem to the radial case and, as a consequence, find an upper bound for the supremum over all functions belonging to the unit ball of Wn;mn (Rn) provided with some specific norm, as well as the sharpness of the constant that appears in Adams inequalities. |
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Macedo, Abiel Costahttp://lattes.cnpq.br/6413790814030608Macedo, Abiel CostaOliveira, José Fransisco Alves deAlbuquerque, José Carloshttp://lattes.cnpq.br/9400644102991942Rocha, Fábio Sodré2018-09-05T11:22:03Z2018-08-10ROCHA, F. S. Desigualdade de Adams em domínios ilimitados. 2018. 86 f. Dissertação (Mestrado em Matemática) - Universidade Federal de Goiás, Goiânia, 2018.http://repositorio.bc.ufg.br/tede/handle/tede/8859ark:/38995/0013000000g7kIn this work our aim is to present an extension of the Trudinger-Moser inequality [20] in unbounded domains of Rn for Sobolev Spaces involving high order derivatives. This inequality is nowadays known as Adams-type inequality [1]. We study the techniques developed in the works due to F. Sani and B. Ruf in [23] and due to N. Lam and G. Lu in [16] which are, essentially, combinations of the Comparison Principle of Trombetti and Vazquez for polyharmonic operators and a symmetrization argument, also known as Schwarz Symmetrization. "With such techniques in hands", our aim is to reduce our problem to the radial case and, as a consequence, find an upper bound for the supremum over all functions belonging to the unit ball of Wn;mn (Rn) provided with some specific norm, as well as the sharpness of the constant that appears in Adams inequalities.Neste trabalho temos como objetivo apresentar uma extensão da desigualdade de AdamsTrudinger-Moser [1] em domínios ilimitados de Rn para espaços de Sobolev envolvendo derivadas de ordem superior no caso crítico. Esta desigualdade é conhecida hoje como desigualdade do tipo Adams [1]. Nosso estudo é baseado nas técnicas desenvolvidas nos trabalhos devidos à F. Sani e B. Ruf em [23] e à N. Lam e G. Lu em [16], que são, essencialmente, combinações do Princípio de Comparação de Vazquez-Trombetti para operadores poliharmônicos e um argumento de simetrização, também conhecido como Simetrização de Schwarz. Munidos de tais técnicas, nosso objetivo é reduzir nosso problema ao caso radial, e como consequência, encontrar um limite superior para o supremo sobre todas as funções pertecentes à bola unitária de Wn;mn (Rn) provido de uma norma específica, bem como também mostrar a otimalidade da constante presente na desigualdade do tipo Adams.Submitted by Liliane Ferreira (ljuvencia30@gmail.com) on 2018-09-05T10:48:04Z No. of bitstreams: 2 Dissertação - Fábio Sodré Rocha - 2018.pdf: 2598970 bytes, checksum: 6dcbeb213d900d41e0a2064ff8a20d22 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5)Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2018-09-05T11:22:03Z (GMT) No. of bitstreams: 2 Dissertação - Fábio Sodré Rocha - 2018.pdf: 2598970 bytes, checksum: 6dcbeb213d900d41e0a2064ff8a20d22 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5)Made available in DSpace on 2018-09-05T11:22:03Z (GMT). No. of bitstreams: 2 Dissertação - Fábio Sodré Rocha - 2018.pdf: 2598970 bytes, checksum: 6dcbeb213d900d41e0a2064ff8a20d22 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2018-08-10Conselho Nacional de Pesquisa e Desenvolvimento Científico e Tecnológico - CNPqapplication/pdfhttp://repositorio.bc.ufg.br/tede/retrieve/49360/Disserta%c3%a7%c3%a3o%20-%20F%c3%a1bio%20Sodr%c3%a9%20Rocha%20-%202018.pdf.jpgporUniversidade Federal de GoiásPrograma de Pós-graduação em Matemática (IME)UFGBrasilInstituto de Matemática e Estatística - IME (RG)http://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessDesigualdade de AdamsCrescimento críticoDesigualdade de Trudinger-MoserEspaços de SobolevSimetrização de SchwarzAdams inequalityCritical growthTrudinger-Moser inequalitySobolev spacesSchwarz symmetrizationCIENCIAS EXATAS E DA TERRA::MATEMATICADesigualdade de Adams em domínios ilimitadosAdams inequality in unbounded domainsinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesis6600717948137941247600600600600-4268777512335152015-7090823417984401694-2555911436985713659reponame:Repositório Institucional da UFGinstname:Universidade Federal de Goiás (UFG)instacron:UFGLICENSElicense.txtlicense.txttext/plain; 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dc.title.eng.fl_str_mv |
Desigualdade de Adams em domínios ilimitados |
dc.title.alternative.eng.fl_str_mv |
Adams inequality in unbounded domains |
title |
Desigualdade de Adams em domínios ilimitados |
spellingShingle |
Desigualdade de Adams em domínios ilimitados Rocha, Fábio Sodré Desigualdade de Adams Crescimento crítico Desigualdade de Trudinger-Moser Espaços de Sobolev Simetrização de Schwarz Adams inequality Critical growth Trudinger-Moser inequality Sobolev spaces Schwarz symmetrization CIENCIAS EXATAS E DA TERRA::MATEMATICA |
title_short |
Desigualdade de Adams em domínios ilimitados |
title_full |
Desigualdade de Adams em domínios ilimitados |
title_fullStr |
Desigualdade de Adams em domínios ilimitados |
title_full_unstemmed |
Desigualdade de Adams em domínios ilimitados |
title_sort |
Desigualdade de Adams em domínios ilimitados |
author |
Rocha, Fábio Sodré |
author_facet |
Rocha, Fábio Sodré |
author_role |
author |
dc.contributor.advisor1.fl_str_mv |
Macedo, Abiel Costa |
dc.contributor.advisor1Lattes.fl_str_mv |
http://lattes.cnpq.br/6413790814030608 |
dc.contributor.referee1.fl_str_mv |
Macedo, Abiel Costa |
dc.contributor.referee2.fl_str_mv |
Oliveira, José Fransisco Alves de |
dc.contributor.referee3.fl_str_mv |
Albuquerque, José Carlos |
dc.contributor.authorLattes.fl_str_mv |
http://lattes.cnpq.br/9400644102991942 |
dc.contributor.author.fl_str_mv |
Rocha, Fábio Sodré |
contributor_str_mv |
Macedo, Abiel Costa Macedo, Abiel Costa Oliveira, José Fransisco Alves de Albuquerque, José Carlos |
dc.subject.por.fl_str_mv |
Desigualdade de Adams Crescimento crítico Desigualdade de Trudinger-Moser Espaços de Sobolev Simetrização de Schwarz |
topic |
Desigualdade de Adams Crescimento crítico Desigualdade de Trudinger-Moser Espaços de Sobolev Simetrização de Schwarz Adams inequality Critical growth Trudinger-Moser inequality Sobolev spaces Schwarz symmetrization CIENCIAS EXATAS E DA TERRA::MATEMATICA |
dc.subject.eng.fl_str_mv |
Adams inequality Critical growth Trudinger-Moser inequality Sobolev spaces Schwarz symmetrization |
dc.subject.cnpq.fl_str_mv |
CIENCIAS EXATAS E DA TERRA::MATEMATICA |
description |
In this work our aim is to present an extension of the Trudinger-Moser inequality [20] in unbounded domains of Rn for Sobolev Spaces involving high order derivatives. This inequality is nowadays known as Adams-type inequality [1]. We study the techniques developed in the works due to F. Sani and B. Ruf in [23] and due to N. Lam and G. Lu in [16] which are, essentially, combinations of the Comparison Principle of Trombetti and Vazquez for polyharmonic operators and a symmetrization argument, also known as Schwarz Symmetrization. "With such techniques in hands", our aim is to reduce our problem to the radial case and, as a consequence, find an upper bound for the supremum over all functions belonging to the unit ball of Wn;mn (Rn) provided with some specific norm, as well as the sharpness of the constant that appears in Adams inequalities. |
publishDate |
2018 |
dc.date.accessioned.fl_str_mv |
2018-09-05T11:22:03Z |
dc.date.issued.fl_str_mv |
2018-08-10 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/masterThesis |
format |
masterThesis |
status_str |
publishedVersion |
dc.identifier.citation.fl_str_mv |
ROCHA, F. S. Desigualdade de Adams em domínios ilimitados. 2018. 86 f. Dissertação (Mestrado em Matemática) - Universidade Federal de Goiás, Goiânia, 2018. |
dc.identifier.uri.fl_str_mv |
http://repositorio.bc.ufg.br/tede/handle/tede/8859 |
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ark:/38995/0013000000g7k |
identifier_str_mv |
ROCHA, F. S. Desigualdade de Adams em domínios ilimitados. 2018. 86 f. Dissertação (Mestrado em Matemática) - Universidade Federal de Goiás, Goiânia, 2018. ark:/38995/0013000000g7k |
url |
http://repositorio.bc.ufg.br/tede/handle/tede/8859 |
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por |
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por |
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Universidade Federal de Goiás |
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UFG |
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Brasil |
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Universidade Federal de Goiás |
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