On the existence of bounded solutions for a nonlinear elliptic system

Autores
Duran, Ricardo Guillermo; Sanmartino, Marcela; Toschi, Marisa
Año de publicación
2011
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
This work deals with the system (−Δ)mu = a(x) vp, (−Δ)mv = b(x) uq with Dirichlet boundary condition in a domain Ω⊂Rn , where Ω is a ball if n ≥ 3 or a smooth perturbation of a ball when n = 2. We prove that, under appropriate conditions on the parameters (a, b, p, q, m, n), any nonnegative solution (u, v) of the system is bounded by a constant independent of (u, v). Moreover, we prove that the conditions are sharp in the sense that, up to some border case, the relation on the parameters are also necessary. The case m = 1 was considered by Souplet (Nonlinear Partial Differ Equ Appl 20:464–479, 2004). Our paper generalize to m ≥ 1 the results of that paper.
Fil: Duran, Ricardo Guillermo. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Sanmartino, Marcela. Universidad Nacional de la Plata. Facultad de Ciencias Exactas. Departamento de Matematicas; Argentina
Fil: Toschi, Marisa. Universidad Nacional del Litoral; Argentina
Materia
Elliptic Systems
A Priori Estimates
Critical Exponents
Weighted Sobolev Spaces
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/14930
Acceder
id CONICETDig_2fb59800487aa29645ba86dfffa44af6
oai_identifier_str oai:ri.conicet.gov.ar:11336/14930
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling On the existence of bounded solutions for a nonlinear elliptic systemDuran, Ricardo GuillermoSanmartino, MarcelaToschi, MarisaElliptic SystemsA Priori EstimatesCritical ExponentsWeighted Sobolev Spaceshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1This work deals with the system (−Δ)mu = a(x) vp, (−Δ)mv = b(x) uq with Dirichlet boundary condition in a domain Ω⊂Rn , where Ω is a ball if n ≥ 3 or a smooth perturbation of a ball when n = 2. We prove that, under appropriate conditions on the parameters (a, b, p, q, m, n), any nonnegative solution (u, v) of the system is bounded by a constant independent of (u, v). Moreover, we prove that the conditions are sharp in the sense that, up to some border case, the relation on the parameters are also necessary. The case m = 1 was considered by Souplet (Nonlinear Partial Differ Equ Appl 20:464–479, 2004). Our paper generalize to m ≥ 1 the results of that paper.Fil: Duran, Ricardo Guillermo. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Sanmartino, Marcela. Universidad Nacional de la Plata. Facultad de Ciencias Exactas. Departamento de Matematicas; ArgentinaFil: Toschi, Marisa. Universidad Nacional del Litoral; ArgentinaSpringer Heidelberg2011-04info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/14930Duran, Ricardo Guillermo; Sanmartino, Marcela; Toschi, Marisa; On the existence of bounded solutions for a nonlinear elliptic system; Springer Heidelberg; Annali Di Matematica Pura Ed Applicata; 191; 4; 4-2011; 771-7820373-3114enginfo:eu-repo/semantics/altIdentifier/url/http://link.springer.com/article/10.1007/s10231-011-0205-2info:eu-repo/semantics/altIdentifier/doi/10.1007/s10231-011-0205-2info:eu-repo/semantics/altIdentifier/url/https://mate.dm.uba.ar/~rduran/papers/dst3.pdfinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:37:28Zoai:ri.conicet.gov.ar:11336/14930instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 10:37:28.37CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv On the existence of bounded solutions for a nonlinear elliptic system
title On the existence of bounded solutions for a nonlinear elliptic system
spellingShingle On the existence of bounded solutions for a nonlinear elliptic system
Duran, Ricardo Guillermo
Elliptic Systems
A Priori Estimates
Critical Exponents
Weighted Sobolev Spaces
title_short On the existence of bounded solutions for a nonlinear elliptic system
title_full On the existence of bounded solutions for a nonlinear elliptic system
title_fullStr On the existence of bounded solutions for a nonlinear elliptic system
title_full_unstemmed On the existence of bounded solutions for a nonlinear elliptic system
title_sort On the existence of bounded solutions for a nonlinear elliptic system
dc.creator.none.fl_str_mv Duran, Ricardo Guillermo
Sanmartino, Marcela
Toschi, Marisa
author Duran, Ricardo Guillermo
author_facet Duran, Ricardo Guillermo
Sanmartino, Marcela
Toschi, Marisa
author_role author
author2 Sanmartino, Marcela
Toschi, Marisa
author2_role author
author
dc.subject.none.fl_str_mv Elliptic Systems
A Priori Estimates
Critical Exponents
Weighted Sobolev Spaces
topic Elliptic Systems
A Priori Estimates
Critical Exponents
Weighted Sobolev Spaces
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv This work deals with the system (−Δ)mu = a(x) vp, (−Δ)mv = b(x) uq with Dirichlet boundary condition in a domain Ω⊂Rn , where Ω is a ball if n ≥ 3 or a smooth perturbation of a ball when n = 2. We prove that, under appropriate conditions on the parameters (a, b, p, q, m, n), any nonnegative solution (u, v) of the system is bounded by a constant independent of (u, v). Moreover, we prove that the conditions are sharp in the sense that, up to some border case, the relation on the parameters are also necessary. The case m = 1 was considered by Souplet (Nonlinear Partial Differ Equ Appl 20:464–479, 2004). Our paper generalize to m ≥ 1 the results of that paper.
Fil: Duran, Ricardo Guillermo. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Sanmartino, Marcela. Universidad Nacional de la Plata. Facultad de Ciencias Exactas. Departamento de Matematicas; Argentina
Fil: Toschi, Marisa. Universidad Nacional del Litoral; Argentina
description This work deals with the system (−Δ)mu = a(x) vp, (−Δ)mv = b(x) uq with Dirichlet boundary condition in a domain Ω⊂Rn , where Ω is a ball if n ≥ 3 or a smooth perturbation of a ball when n = 2. We prove that, under appropriate conditions on the parameters (a, b, p, q, m, n), any nonnegative solution (u, v) of the system is bounded by a constant independent of (u, v). Moreover, we prove that the conditions are sharp in the sense that, up to some border case, the relation on the parameters are also necessary. The case m = 1 was considered by Souplet (Nonlinear Partial Differ Equ Appl 20:464–479, 2004). Our paper generalize to m ≥ 1 the results of that paper.
publishDate 2011
dc.date.none.fl_str_mv 2011-04
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/14930
Duran, Ricardo Guillermo; Sanmartino, Marcela; Toschi, Marisa; On the existence of bounded solutions for a nonlinear elliptic system; Springer Heidelberg; Annali Di Matematica Pura Ed Applicata; 191; 4; 4-2011; 771-782
0373-3114
url http://hdl.handle.net/11336/14930
identifier_str_mv Duran, Ricardo Guillermo; Sanmartino, Marcela; Toschi, Marisa; On the existence of bounded solutions for a nonlinear elliptic system; Springer Heidelberg; Annali Di Matematica Pura Ed Applicata; 191; 4; 4-2011; 771-782
0373-3114
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://link.springer.com/article/10.1007/s10231-011-0205-2
info:eu-repo/semantics/altIdentifier/doi/10.1007/s10231-011-0205-2
info:eu-repo/semantics/altIdentifier/url/https://mate.dm.uba.ar/~rduran/papers/dst3.pdf
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Springer Heidelberg
publisher.none.fl_str_mv Springer Heidelberg
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
_version_ 1844614395088338944
score 13.070432

Publicaciones similares