Cohomology and partial differential equations

Detalhes bibliográficos
Ano de defesa: 2024
Autor(a) principal: Marinho, Artur Jorge lattes
Orientador(a): Silva, Kaye Oliveira da lattes
Banca de defesa: Silva, Kaye Oliveira da, Siciliano, Gaetano, Macedo, Abiel Costa
Tipo de documento: Dissertação
Tipo de acesso: Acesso aberto
dARK ID: ark:/38995/001300000b7tj
Idioma: eng
Instituição de defesa: Universidade Federal de Goiás
Programa de Pós-Graduação: Programa de Pós-graduação em Matemática (IME)
Departamento: Instituto de Matemática e Estatística - IME (RMG)
País: Brasil
Palavras-chave em Português:
Teoria de Morse
Índice cohomológico
P-Laplaciano
Equações diferenciais parciais elípticas
Enlace
Pontos críticos
Métodos variacionais
Palavras-chave em Inglês:
Morse theory
Cohomological index
P-Laplacian
Brezis-Niremberg problem
Elliptic partial differential equations
Linking
Critical points
Variational methods
Área do conhecimento CNPq:
CIENCIAS EXATAS E DA TERRA::MATEMATICA
Link de acesso: http://repositorio.bc.ufg.br/tede/handle/tede/13453
Resumo: This text deals with elliptic partial differential equation problems by the Morse theoric point of view. Since Morse theory has a connection with some concepts from algebraic topology, cohomology theory is employed to show existence result for a class of equations. The concept of cohomological index will be useful to show multiple solution results for the Brezis-Nirenberg problem for the p-Laplacian.
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spelling Silva, Kaye Oliveira dahttp://lattes.cnpq.br/3634338534144726Silva, Kaye Oliveira daSiciliano, GaetanoMacedo, Abiel Costahttp://lattes.cnpq.br/9911806116283135Marinho, Artur Jorge2024-10-02T17:09:14Z2024-10-02T17:09:14Z2024-06-20MARINHO, A. J. Cohomology and partial differential equations. 2024. 141 f. Dissertação (Mestrado em Matemática) - Instituto de Matemática e Estatística, Universidade Federal de Goiás, Goiânia, 2024.http://repositorio.bc.ufg.br/tede/handle/tede/13453ark:/38995/001300000b7tjThis text deals with elliptic partial differential equation problems by the Morse theoric point of view. Since Morse theory has a connection with some concepts from algebraic topology, cohomology theory is employed to show existence result for a class of equations. The concept of cohomological index will be useful to show multiple solution results for the Brezis-Nirenberg problem for the p-Laplacian.Este texto trata de problemas de equações diferenciais parciais elípticas do ponto de vista da teoria de Morse. Como a teoria de Morse tem uma conexão com alguns conceitos da topologia algébrica, a teoria da cohomologia é empregada para mostrar um resultado de existência para uma classe de equações. O conceito de índice cohomológico será útil para mostrar resultados de múltiplas soluções para o problema de Brezis-Nirenberg para o p-Laplaciano.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPESengUniversidade Federal de GoiásPrograma de Pós-graduação em Matemática (IME)UFGBrasilInstituto de Matemática e Estatística - IME (RMG)Attribution-NonCommercial-NoDerivatives 4.0 Internationalinfo:eu-repo/semantics/openAccessMorse theoryCohomological indexP-LaplacianBrezis-Niremberg problemElliptic partial differential equationsLinkingCritical pointsVariational methodsTeoria de MorseÍndice cohomológicoP-LaplacianoEquações diferenciais parciais elípticasEnlacePontos críticosMétodos variacionaisCIENCIAS EXATAS E DA TERRA::MATEMATICACohomology and partial differential equationsCohomologia e equações diferenciais parciaisinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisreponame:Repositório Institucional da UFGinstname:Universidade Federal de Goiás (UFG)instacron:UFGLICENSElicense.txtlicense.txttext/plain; charset=utf-81748http://repositorio.bc.ufg.br/tede/bitstreams/f7afdf38-a23d-4683-a06f-30eea3a05b00/download8a4605be74aa9ea9d79846c1fba20a33MD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8805http://repositorio.bc.ufg.br/tede/bitstreams/474213e3-637d-4532-ba07-012a71087b1a/download4460e5956bc1d1639be9ae6146a50347MD52ORIGINALDissertação - Artur Jorge Marinho - 2024.pdfDissertação - Artur Jorge Marinho - 2024.pdfapplication/pdf1449024http://repositorio.bc.ufg.br/tede/bitstreams/74c17c73-a7a8-4c04-94ca-b4bcd45dbfbb/download2ca9400e0e077056a2076afb9ddcf932MD53tede/134532024-10-02 14:09:14.883http://creativecommons.org/licenses/by-nc-nd/4.0/Attribution-NonCommercial-NoDerivatives 4.0 Internationalopen.accessoai:repositorio.bc.ufg.br:tede/13453http://repositorio.bc.ufg.br/tedeRepositório InstitucionalPUBhttps://repositorio.bc.ufg.br/tedeserver/oai/requestgrt.bc@ufg.bropendoar:oai:repositorio.bc.ufg.br:tede/12342024-10-02T17:09:14Repositório Institucional da UFG - Universidade Federal de Goiás (UFG)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
dc.title.none.fl_str_mv Cohomology and partial differential equations
dc.title.alternative.por.fl_str_mv Cohomologia e equações diferenciais parciais
title Cohomology and partial differential equations
spellingShingle Cohomology and partial differential equations
Marinho, Artur Jorge
Morse theory
Cohomological index
P-Laplacian
Brezis-Niremberg problem
Elliptic partial differential equations
Linking
Critical points
Variational methods
Teoria de Morse
Índice cohomológico
P-Laplaciano
Equações diferenciais parciais elípticas
Enlace
Pontos críticos
Métodos variacionais
CIENCIAS EXATAS E DA TERRA::MATEMATICA
title_short Cohomology and partial differential equations
title_full Cohomology and partial differential equations
title_fullStr Cohomology and partial differential equations
title_full_unstemmed Cohomology and partial differential equations
title_sort Cohomology and partial differential equations
author Marinho, Artur Jorge
author_facet Marinho, Artur Jorge
author_role author
dc.contributor.advisor1.fl_str_mv Silva, Kaye Oliveira da
dc.contributor.advisor1Lattes.fl_str_mv http://lattes.cnpq.br/3634338534144726
dc.contributor.referee1.fl_str_mv Silva, Kaye Oliveira da
dc.contributor.referee2.fl_str_mv Siciliano, Gaetano
dc.contributor.referee3.fl_str_mv Macedo, Abiel Costa
dc.contributor.authorLattes.fl_str_mv http://lattes.cnpq.br/9911806116283135
dc.contributor.author.fl_str_mv Marinho, Artur Jorge
contributor_str_mv Silva, Kaye Oliveira da
Silva, Kaye Oliveira da
Siciliano, Gaetano
Macedo, Abiel Costa
dc.subject.eng.fl_str_mv Morse theory
Cohomological index
P-Laplacian
Brezis-Niremberg problem
Elliptic partial differential equations
Linking
Critical points
Variational methods
topic Morse theory
Cohomological index
P-Laplacian
Brezis-Niremberg problem
Elliptic partial differential equations
Linking
Critical points
Variational methods
Teoria de Morse
Índice cohomológico
P-Laplaciano
Equações diferenciais parciais elípticas
Enlace
Pontos críticos
Métodos variacionais
CIENCIAS EXATAS E DA TERRA::MATEMATICA
dc.subject.por.fl_str_mv Teoria de Morse
Índice cohomológico
P-Laplaciano
Equações diferenciais parciais elípticas
Enlace
Pontos críticos
Métodos variacionais
dc.subject.cnpq.fl_str_mv CIENCIAS EXATAS E DA TERRA::MATEMATICA
description This text deals with elliptic partial differential equation problems by the Morse theoric point of view. Since Morse theory has a connection with some concepts from algebraic topology, cohomology theory is employed to show existence result for a class of equations. The concept of cohomological index will be useful to show multiple solution results for the Brezis-Nirenberg problem for the p-Laplacian.
publishDate 2024
dc.date.accessioned.fl_str_mv 2024-10-02T17:09:14Z
dc.date.available.fl_str_mv 2024-10-02T17:09:14Z
dc.date.issued.fl_str_mv 2024-06-20
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 MARINHO, A. J. Cohomology and partial differential equations. 2024. 141 f. Dissertação (Mestrado em Matemática) - Instituto de Matemática e Estatística, Universidade Federal de Goiás, Goiânia, 2024.
dc.identifier.uri.fl_str_mv http://repositorio.bc.ufg.br/tede/handle/tede/13453
dc.identifier.dark.fl_str_mv ark:/38995/001300000b7tj
identifier_str_mv MARINHO, A. J. Cohomology and partial differential equations. 2024. 141 f. Dissertação (Mestrado em Matemática) - Instituto de Matemática e Estatística, Universidade Federal de Goiás, Goiânia, 2024.
ark:/38995/001300000b7tj
url http://repositorio.bc.ufg.br/tede/handle/tede/13453
dc.language.iso.fl_str_mv eng
language eng
dc.rights.driver.fl_str_mv Attribution-NonCommercial-NoDerivatives 4.0 International
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Attribution-NonCommercial-NoDerivatives 4.0 International
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Universidade Federal de Goiás
dc.publisher.program.fl_str_mv Programa de Pós-graduação em Matemática (IME)
dc.publisher.initials.fl_str_mv UFG
dc.publisher.country.fl_str_mv Brasil
dc.publisher.department.fl_str_mv Instituto de Matemática e Estatística - IME (RMG)
publisher.none.fl_str_mv Universidade Federal de Goiás
dc.source.none.fl_str_mv reponame:Repositório Institucional da UFG
instname:Universidade Federal de Goiás (UFG)
instacron:UFG
instname_str Universidade Federal de Goiás (UFG)
instacron_str UFG
institution UFG
reponame_str Repositório Institucional da UFG
collection Repositório Institucional da UFG
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