Computing the first eigenvalue of the p-Laplacian via the inverse power method.

Detalhes bibliográficos
Autor(a) principal: Biezuner, Rodney Josué
Data de Publicação: 2009
Outros Autores: Ercole, Grey, Martins, Eder Marinho
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UFOP
Texto Completo: http://www.repositorio.ufop.br/handle/123456789/1970
Resumo: In this paper, we discuss a new method for computing the first Dirichlet eigenvalue of the p-Laplacian inspired by the inverse power method in finite dimensional linear algebra. The iterative technique is independent of the particular method used in solving the p-Laplacian equation and therefore can be made as efficient as the latter. The method is validated theoretically for any ball in Rn if p >1 and for any bounded domain in the particular case p = 2. For p >2 the method is validated numerically for the square.
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spelling Biezuner, Rodney JosuéErcole, GreyMartins, Eder Marinho2012-12-05T15:50:55Z2012-12-05T15:50:55Z2009BIEZUNER, R. J.; ERCOLE, G.; MARTINS, E. M. Computing the first eigenvalue of the p-Laplacian via the inverse power method. Journal of Functional Analysis, v. 257, n. 1, p. 243-270, 2009. Disponível em: <https://www.sciencedirect.com/science/article/pii/S0022123609000445>. Acesso em: 03 dez. 201200221236http://www.repositorio.ufop.br/handle/123456789/1970In this paper, we discuss a new method for computing the first Dirichlet eigenvalue of the p-Laplacian inspired by the inverse power method in finite dimensional linear algebra. The iterative technique is independent of the particular method used in solving the p-Laplacian equation and therefore can be made as efficient as the latter. The method is validated theoretically for any ball in Rn if p >1 and for any bounded domain in the particular case p = 2. For p >2 the method is validated numerically for the square.p-LaplacianFirst eigenvalueComparison principlePower methodComputing the first eigenvalue of the p-Laplacian via the inverse power method.info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleO periódico Journal of Functional Analysis concede permissão para depósito do artigo no Repositório Institucional da UFOP. Número da licença: 3305300201996.info:eu-repo/semantics/openAccessengreponame:Repositório Institucional da UFOPinstname:Universidade Federal de Ouro Preto (UFOP)instacron:UFOPLICENSElicense.txtlicense.txttext/plain; charset=utf-81748http://www.repositorio.ufop.br/bitstream/123456789/1970/2/license.txt8a4605be74aa9ea9d79846c1fba20a33MD52ORIGINALARTIGO_ComputingFirstEigenvalue.pdfARTIGO_ComputingFirstEigenvalue.pdfapplication/pdf286628http://www.repositorio.ufop.br/bitstream/123456789/1970/1/ARTIGO_ComputingFirstEigenvalue.pdfcc10afa1056273eda183f9aea7f18401MD51123456789/19702019-03-15 13:01:22.911oai:localhost: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Repositório InstitucionalPUBhttp://www.repositorio.ufop.br/oai/requestrepositorio@ufop.edu.bropendoar:32332019-03-15T17:01:22Repositório Institucional da UFOP - Universidade Federal de Ouro Preto (UFOP)false
dc.title.pt_BR.fl_str_mv Computing the first eigenvalue of the p-Laplacian via the inverse power method.
title Computing the first eigenvalue of the p-Laplacian via the inverse power method.
spellingShingle Computing the first eigenvalue of the p-Laplacian via the inverse power method.
Biezuner, Rodney Josué
p-Laplacian
First eigenvalue
Comparison principle
Power method
title_short Computing the first eigenvalue of the p-Laplacian via the inverse power method.
title_full Computing the first eigenvalue of the p-Laplacian via the inverse power method.
title_fullStr Computing the first eigenvalue of the p-Laplacian via the inverse power method.
title_full_unstemmed Computing the first eigenvalue of the p-Laplacian via the inverse power method.
title_sort Computing the first eigenvalue of the p-Laplacian via the inverse power method.
author Biezuner, Rodney Josué
author_facet Biezuner, Rodney Josué
Ercole, Grey
Martins, Eder Marinho
author_role author
author2 Ercole, Grey
Martins, Eder Marinho
author2_role author
author
dc.contributor.author.fl_str_mv Biezuner, Rodney Josué
Ercole, Grey
Martins, Eder Marinho
dc.subject.por.fl_str_mv p-Laplacian
First eigenvalue
Comparison principle
Power method
topic p-Laplacian
First eigenvalue
Comparison principle
Power method
description In this paper, we discuss a new method for computing the first Dirichlet eigenvalue of the p-Laplacian inspired by the inverse power method in finite dimensional linear algebra. The iterative technique is independent of the particular method used in solving the p-Laplacian equation and therefore can be made as efficient as the latter. The method is validated theoretically for any ball in Rn if p >1 and for any bounded domain in the particular case p = 2. For p >2 the method is validated numerically for the square.
publishDate 2009
dc.date.issued.fl_str_mv 2009
dc.date.accessioned.fl_str_mv 2012-12-05T15:50:55Z
dc.date.available.fl_str_mv 2012-12-05T15:50:55Z
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.citation.fl_str_mv BIEZUNER, R. J.; ERCOLE, G.; MARTINS, E. M. Computing the first eigenvalue of the p-Laplacian via the inverse power method. Journal of Functional Analysis, v. 257, n. 1, p. 243-270, 2009. Disponível em: <https://www.sciencedirect.com/science/article/pii/S0022123609000445>. Acesso em: 03 dez. 2012
dc.identifier.uri.fl_str_mv http://www.repositorio.ufop.br/handle/123456789/1970
dc.identifier.issn.none.fl_str_mv 00221236
identifier_str_mv BIEZUNER, R. J.; ERCOLE, G.; MARTINS, E. M. Computing the first eigenvalue of the p-Laplacian via the inverse power method. Journal of Functional Analysis, v. 257, n. 1, p. 243-270, 2009. Disponível em: <https://www.sciencedirect.com/science/article/pii/S0022123609000445>. Acesso em: 03 dez. 2012
00221236
url http://www.repositorio.ufop.br/handle/123456789/1970
dc.language.iso.fl_str_mv eng
language eng
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.source.none.fl_str_mv reponame:Repositório Institucional da UFOP
instname:Universidade Federal de Ouro Preto (UFOP)
instacron:UFOP
instname_str Universidade Federal de Ouro Preto (UFOP)
instacron_str UFOP
institution UFOP
reponame_str Repositório Institucional da UFOP
collection Repositório Institucional da UFOP
bitstream.url.fl_str_mv http://www.repositorio.ufop.br/bitstream/123456789/1970/2/license.txt
http://www.repositorio.ufop.br/bitstream/123456789/1970/1/ARTIGO_ComputingFirstEigenvalue.pdf
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repository.name.fl_str_mv Repositório Institucional da UFOP - Universidade Federal de Ouro Preto (UFOP)
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