Recent Results on a Generalization of the Laplacian

Detalhes bibliográficos
Autor(a) principal: SIMAS,A.B.
Data de Publicação: 2015
Outros Autores: VALENTIM,F.J.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)
Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512015000200131
Resumo: In this paper we discuss recent results regarding a generalization of the Laplacian. To be more precise, fix a function W(x1, ..., xd) = Σdk=1 Wk(xk), where each Wk : ℝ → ℝ is a right continuous with left limits and strictly increasing function. Using W, we construct the generalized laplacian ℒW = Σdi=1 ∂xi ∂wi, where ∂wi is a generalized differential operator induced by the function Wi. We present results on spectral properties of ℒW, Sobolev spaces induced by ℒW(W-Sobolev spaces), generalized partial differential equations, generalized stochastic differential equations and stochastic homogenization.
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spelling Recent Results on a Generalization of the LaplacianW-Sobolev spacegeneralized Laplacianhomogenizationpartial differential equationsIn this paper we discuss recent results regarding a generalization of the Laplacian. To be more precise, fix a function W(x1, ..., xd) = Σdk=1 Wk(xk), where each Wk : ℝ → ℝ is a right continuous with left limits and strictly increasing function. Using W, we construct the generalized laplacian ℒW = Σdi=1 ∂xi ∂wi, where ∂wi is a generalized differential operator induced by the function Wi. We present results on spectral properties of ℒW, Sobolev spaces induced by ℒW(W-Sobolev spaces), generalized partial differential equations, generalized stochastic differential equations and stochastic homogenization.Sociedade Brasileira de Matemática Aplicada e Computacional2015-08-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512015000200131TEMA (São Carlos) v.16 n.2 2015reponame:TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)instname:Sociedade Brasileira de Matemática Aplicada e Computacionalinstacron:SBMAC10.5540/tema.2015.016.02.0131info:eu-repo/semantics/openAccessSIMAS,A.B.VALENTIM,F.J.eng2015-09-15T00:00:00Zoai:scielo:S2179-84512015000200131Revistahttp://www.scielo.br/temaPUBhttps://old.scielo.br/oai/scielo-oai.phpcastelo@icmc.usp.br2179-84511677-1966opendoar:2015-09-15T00:00TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online) - Sociedade Brasileira de Matemática Aplicada e Computacionalfalse
dc.title.none.fl_str_mv Recent Results on a Generalization of the Laplacian
title Recent Results on a Generalization of the Laplacian
spellingShingle Recent Results on a Generalization of the Laplacian
SIMAS,A.B.
W-Sobolev space
generalized Laplacian
homogenization
partial differential equations
title_short Recent Results on a Generalization of the Laplacian
title_full Recent Results on a Generalization of the Laplacian
title_fullStr Recent Results on a Generalization of the Laplacian
title_full_unstemmed Recent Results on a Generalization of the Laplacian
title_sort Recent Results on a Generalization of the Laplacian
author SIMAS,A.B.
author_facet SIMAS,A.B.
VALENTIM,F.J.
author_role author
author2 VALENTIM,F.J.
author2_role author
dc.contributor.author.fl_str_mv SIMAS,A.B.
VALENTIM,F.J.
dc.subject.por.fl_str_mv W-Sobolev space
generalized Laplacian
homogenization
partial differential equations
topic W-Sobolev space
generalized Laplacian
homogenization
partial differential equations
description In this paper we discuss recent results regarding a generalization of the Laplacian. To be more precise, fix a function W(x1, ..., xd) = Σdk=1 Wk(xk), where each Wk : ℝ → ℝ is a right continuous with left limits and strictly increasing function. Using W, we construct the generalized laplacian ℒW = Σdi=1 ∂xi ∂wi, where ∂wi is a generalized differential operator induced by the function Wi. We present results on spectral properties of ℒW, Sobolev spaces induced by ℒW(W-Sobolev spaces), generalized partial differential equations, generalized stochastic differential equations and stochastic homogenization.
publishDate 2015
dc.date.none.fl_str_mv 2015-08-01
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512015000200131
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512015000200131
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.5540/tema.2015.016.02.0131
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv text/html
dc.publisher.none.fl_str_mv Sociedade Brasileira de Matemática Aplicada e Computacional
publisher.none.fl_str_mv Sociedade Brasileira de Matemática Aplicada e Computacional
dc.source.none.fl_str_mv TEMA (São Carlos) v.16 n.2 2015
reponame:TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)
instname:Sociedade Brasileira de Matemática Aplicada e Computacional
instacron:SBMAC
instname_str Sociedade Brasileira de Matemática Aplicada e Computacional
instacron_str SBMAC
institution SBMAC
reponame_str TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)
collection TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)
repository.name.fl_str_mv TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online) - Sociedade Brasileira de Matemática Aplicada e Computacional
repository.mail.fl_str_mv castelo@icmc.usp.br
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