Sub-supersolution method for a quasilinear elliptic problem involving the 1-laplacian operator and a gradient term

Detalhes bibliográficos
Autor(a) principal: Figueiredo, Giovany M.
Data de Publicação: 2020
Outros Autores: Pimenta, Marcos T.O. [UNESP]
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.1016/j.jfa.2019.108325
http://hdl.handle.net/11449/197957
Resumo: In this work we study a quasilinear elliptic problem involving the 1-laplacian operator and a gradient term. The problem requires the definition of a suitable sense of solution, which allows us to show the existence of a solution in BV(Ω), having no jump part. Despite the lack of regularity of the solutions, we develop a sub-supersolution approach, together with a thorough analysis of the distributional derivative of the functions in BV(Ω).
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spelling Sub-supersolution method for a quasilinear elliptic problem involving the 1-laplacian operator and a gradient term1-Laplacian operatorFunctions of bounded variationSub-supersolution methodIn this work we study a quasilinear elliptic problem involving the 1-laplacian operator and a gradient term. The problem requires the definition of a suitable sense of solution, which allows us to show the existence of a solution in BV(Ω), having no jump part. Despite the lack of regularity of the solutions, we develop a sub-supersolution approach, together with a thorough analysis of the distributional derivative of the functions in BV(Ω).Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Apoio à Pesquisa do Distrito FederalFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Departamento de Matemática Universidade de Brasilia - UNBDepartamento de Matemática e Computação Universidade Estadual Paulista - UnespDepartamento de Matemática e Computação Universidade Estadual Paulista - UnespFAPESP: 2019/14330-9Universidade de Brasília (UnB)Universidade Estadual Paulista (Unesp)Figueiredo, Giovany M.Pimenta, Marcos T.O. [UNESP]2020-12-12T00:55:05Z2020-12-12T00:55:05Z2020-02-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://dx.doi.org/10.1016/j.jfa.2019.108325Journal of Functional Analysis, v. 278, n. 3, 2020.1096-07830022-1236http://hdl.handle.net/11449/19795710.1016/j.jfa.2019.1083252-s2.0-85072603527Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengJournal of Functional Analysisinfo:eu-repo/semantics/openAccess2021-10-23T07:27:32Zoai:repositorio.unesp.br:11449/197957Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462021-10-23T07:27:32Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Sub-supersolution method for a quasilinear elliptic problem involving the 1-laplacian operator and a gradient term
title Sub-supersolution method for a quasilinear elliptic problem involving the 1-laplacian operator and a gradient term
spellingShingle Sub-supersolution method for a quasilinear elliptic problem involving the 1-laplacian operator and a gradient term
Figueiredo, Giovany M.
1-Laplacian operator
Functions of bounded variation
Sub-supersolution method
title_short Sub-supersolution method for a quasilinear elliptic problem involving the 1-laplacian operator and a gradient term
title_full Sub-supersolution method for a quasilinear elliptic problem involving the 1-laplacian operator and a gradient term
title_fullStr Sub-supersolution method for a quasilinear elliptic problem involving the 1-laplacian operator and a gradient term
title_full_unstemmed Sub-supersolution method for a quasilinear elliptic problem involving the 1-laplacian operator and a gradient term
title_sort Sub-supersolution method for a quasilinear elliptic problem involving the 1-laplacian operator and a gradient term
author Figueiredo, Giovany M.
author_facet Figueiredo, Giovany M.
Pimenta, Marcos T.O. [UNESP]
author_role author
author2 Pimenta, Marcos T.O. [UNESP]
author2_role author
dc.contributor.none.fl_str_mv Universidade de Brasília (UnB)
Universidade Estadual Paulista (Unesp)
dc.contributor.author.fl_str_mv Figueiredo, Giovany M.
Pimenta, Marcos T.O. [UNESP]
dc.subject.por.fl_str_mv 1-Laplacian operator
Functions of bounded variation
Sub-supersolution method
topic 1-Laplacian operator
Functions of bounded variation
Sub-supersolution method
description In this work we study a quasilinear elliptic problem involving the 1-laplacian operator and a gradient term. The problem requires the definition of a suitable sense of solution, which allows us to show the existence of a solution in BV(Ω), having no jump part. Despite the lack of regularity of the solutions, we develop a sub-supersolution approach, together with a thorough analysis of the distributional derivative of the functions in BV(Ω).
publishDate 2020
dc.date.none.fl_str_mv 2020-12-12T00:55:05Z
2020-12-12T00:55:05Z
2020-02-01
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://dx.doi.org/10.1016/j.jfa.2019.108325
Journal of Functional Analysis, v. 278, n. 3, 2020.
1096-0783
0022-1236
http://hdl.handle.net/11449/197957
10.1016/j.jfa.2019.108325
2-s2.0-85072603527
url http://dx.doi.org/10.1016/j.jfa.2019.108325
http://hdl.handle.net/11449/197957
identifier_str_mv Journal of Functional Analysis, v. 278, n. 3, 2020.
1096-0783
0022-1236
10.1016/j.jfa.2019.108325
2-s2.0-85072603527
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Journal of Functional Analysis
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.source.none.fl_str_mv Scopus
reponame:Repositório Institucional da UNESP
instname:Universidade Estadual Paulista (UNESP)
instacron:UNESP
instname_str Universidade Estadual Paulista (UNESP)
instacron_str UNESP
institution UNESP
reponame_str Repositório Institucional da UNESP
collection Repositório Institucional da UNESP
repository.name.fl_str_mv Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)
repository.mail.fl_str_mv
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