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Quasilinear elliptic systems involving the 1-Laplacian operator with subcritical and critical nonlinearities

Bibliographic Details
Main Author: Carranza, Yino B. Cueva [UNESP]
Publication Date: 2024
Other Authors: Pimenta, Marcos T. O. [UNESP]
Format: Article
Language: eng
Source: Repositório Institucional da UNESP
Download full: http://dx.doi.org/10.1007/s12215-023-00969-2
https://hdl.handle.net/11449/304399
Summary: In this paper, we study some systems of elliptic PDEs involving the 1-Laplacian operator. In the first one, we deal with the subcritical regime, while in the second, we study a system with nonlinearities with critical growth. The approach is based on an approximation argument, in which the solutions are obtained as the limit of related problems with the p-Laplacian operator. In order to overcome the lack of compactness in the critical case, a version of the Concentration of Compactness Principle of Lions is proved.
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spelling Quasilinear elliptic systems involving the 1-Laplacian operator with subcritical and critical nonlinearities1-Laplacian operator35J6235J75Critical nonlinearitiesElliptic systemsSpace of functions of bounded variationIn this paper, we study some systems of elliptic PDEs involving the 1-Laplacian operator. In the first one, we deal with the subcritical regime, while in the second, we study a system with nonlinearities with critical growth. The approach is based on an approximation argument, in which the solutions are obtained as the limit of related problems with the p-Laplacian operator. In order to overcome the lack of compactness in the critical case, a version of the Concentration of Compactness Principle of Lions is proved.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Departamento de Matemática Intituto de Biociências Letras e Ciências Exatas Universidade Estadual Paulista - Unesp, SPDepartamento de Matemática e Computação Faculdade de Ciências e Tecnologia Universidade Estadual Paulista - Unesp, SPDepartamento de Matemática Intituto de Biociências Letras e Ciências Exatas Universidade Estadual Paulista - Unesp, SPDepartamento de Matemática e Computação Faculdade de Ciências e Tecnologia Universidade Estadual Paulista - Unesp, SPCAPES: 001FAPESP: 2021/04158-4CNPq: 304765/2021-0Universidade Estadual Paulista (UNESP)Carranza, Yino B. Cueva [UNESP]Pimenta, Marcos T. O. [UNESP]2025-04-29T19:34:49Z2024-04-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article1037-1058http://dx.doi.org/10.1007/s12215-023-00969-2Rendiconti del Circolo Matematico di Palermo, v. 73, n. 3, p. 1037-1058, 2024.1973-44090009-725Xhttps://hdl.handle.net/11449/30439910.1007/s12215-023-00969-22-s2.0-85176777272Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengRendiconti del Circolo Matematico di Palermoinfo:eu-repo/semantics/openAccess2025-04-30T13:52:46Zoai:repositorio.unesp.br:11449/304399Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestrepositoriounesp@unesp.bropendoar:29462025-04-30T13:52:46Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Quasilinear elliptic systems involving the 1-Laplacian operator with subcritical and critical nonlinearities
title Quasilinear elliptic systems involving the 1-Laplacian operator with subcritical and critical nonlinearities
spellingShingle Quasilinear elliptic systems involving the 1-Laplacian operator with subcritical and critical nonlinearities
Carranza, Yino B. Cueva [UNESP]
1-Laplacian operator
35J62
35J75
Critical nonlinearities
Elliptic systems
Space of functions of bounded variation
title_short Quasilinear elliptic systems involving the 1-Laplacian operator with subcritical and critical nonlinearities
title_full Quasilinear elliptic systems involving the 1-Laplacian operator with subcritical and critical nonlinearities
title_fullStr Quasilinear elliptic systems involving the 1-Laplacian operator with subcritical and critical nonlinearities
title_full_unstemmed Quasilinear elliptic systems involving the 1-Laplacian operator with subcritical and critical nonlinearities
title_sort Quasilinear elliptic systems involving the 1-Laplacian operator with subcritical and critical nonlinearities
author Carranza, Yino B. Cueva [UNESP]
author_facet Carranza, Yino B. Cueva [UNESP]
Pimenta, Marcos T. O. [UNESP]
author_role author
author2 Pimenta, Marcos T. O. [UNESP]
author2_role author
dc.contributor.none.fl_str_mv Universidade Estadual Paulista (UNESP)
dc.contributor.author.fl_str_mv Carranza, Yino B. Cueva [UNESP]
Pimenta, Marcos T. O. [UNESP]
dc.subject.por.fl_str_mv 1-Laplacian operator
35J62
35J75
Critical nonlinearities
Elliptic systems
Space of functions of bounded variation
topic 1-Laplacian operator
35J62
35J75
Critical nonlinearities
Elliptic systems
Space of functions of bounded variation
description In this paper, we study some systems of elliptic PDEs involving the 1-Laplacian operator. In the first one, we deal with the subcritical regime, while in the second, we study a system with nonlinearities with critical growth. The approach is based on an approximation argument, in which the solutions are obtained as the limit of related problems with the p-Laplacian operator. In order to overcome the lack of compactness in the critical case, a version of the Concentration of Compactness Principle of Lions is proved.
publishDate 2024
dc.date.none.fl_str_mv 2024-04-01
2025-04-29T19:34:49Z
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/10.1007/s12215-023-00969-2
Rendiconti del Circolo Matematico di Palermo, v. 73, n. 3, p. 1037-1058, 2024.
1973-4409
0009-725X
https://hdl.handle.net/11449/304399
10.1007/s12215-023-00969-2
2-s2.0-85176777272
url http://dx.doi.org/10.1007/s12215-023-00969-2
https://hdl.handle.net/11449/304399
identifier_str_mv Rendiconti del Circolo Matematico di Palermo, v. 73, n. 3, p. 1037-1058, 2024.
1973-4409
0009-725X
10.1007/s12215-023-00969-2
2-s2.0-85176777272
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Rendiconti del Circolo Matematico di Palermo
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 1037-1058
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 repositoriounesp@unesp.br
_version_ 1834482869037170688

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