The limit as p→ ∞ in the eigenvalue problem for a system of p-Laplacians

Autores
Bonheure, Denis; Rossi, Julio Daniel; Saintier, Nicolas Bernard Claude
Año de publicación
2016
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper, we study the behavior as p→ ∞ of eigenvalues and eigenfunctions of a system of p-Laplacians, that is (Formula presented.) in a bounded smooth domain Ω. Here α+ β= p. We assume that α/p→Γ and β/p→1-Γ as p→ ∞ and we prove that for the first eigenvalue λ1,p we have (λ1,p)1/p→λ∞=1/maxx∈Ωdist(x,∂Ω).Concerning the eigenfunctions (up, vp) associated with λ1,p normalized by ∫Ω|up|α|vp|β=1, there is a uniform limit (u∞, v∞) that is a solution to a limit minimization problem as well as a viscosity solution to (Formula presented.) In addition, we also analyze the limit PDE when we consider higher eigenvalues.
Fil: Bonheure, Denis. Université Libre de Bruxelles; Bélgica
Fil: Rossi, Julio Daniel. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Saintier, Nicolas Bernard Claude. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
INFINITY LAPLACIAN
NONLINEAR EIGENVALUE PROBLEM
P-LAPLACIAN
VISCOSITY SOLUTIONS
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:11336/59873
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/59873
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling The limit as p→ ∞ in the eigenvalue problem for a system of p-LaplaciansBonheure, DenisRossi, Julio DanielSaintier, Nicolas Bernard ClaudeINFINITY LAPLACIANNONLINEAR EIGENVALUE PROBLEMP-LAPLACIANVISCOSITY SOLUTIONShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this paper, we study the behavior as p→ ∞ of eigenvalues and eigenfunctions of a system of p-Laplacians, that is (Formula presented.) in a bounded smooth domain Ω. Here α+ β= p. We assume that α/p→Γ and β/p→1-Γ as p→ ∞ and we prove that for the first eigenvalue λ1,p we have (λ1,p)1/p→λ∞=1/maxx∈Ωdist(x,∂Ω).Concerning the eigenfunctions (up, vp) associated with λ1,p normalized by ∫Ω|up|α|vp|β=1, there is a uniform limit (u∞, v∞) that is a solution to a limit minimization problem as well as a viscosity solution to (Formula presented.) In addition, we also analyze the limit PDE when we consider higher eigenvalues.Fil: Bonheure, Denis. Université Libre de Bruxelles; BélgicaFil: Rossi, Julio Daniel. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Saintier, Nicolas Bernard Claude. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaSpringer Heidelberg2016-10info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/59873Bonheure, Denis; Rossi, Julio Daniel; Saintier, Nicolas Bernard Claude; The limit as p→ ∞ in the eigenvalue problem for a system of p-Laplacians; Springer Heidelberg; Annali Di Matematica Pura Ed Applicata; 195; 5; 10-2016; 1771-17850373-31141618-1891CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1007/s10231-015-0547-2info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s10231-015-0547-2info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:55:17Zoai:ri.conicet.gov.ar:11336/59873instacron: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:34982025-09-03 09:55:17.839CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv The limit as p→ ∞ in the eigenvalue problem for a system of p-Laplacians
title The limit as p→ ∞ in the eigenvalue problem for a system of p-Laplacians
spellingShingle The limit as p→ ∞ in the eigenvalue problem for a system of p-Laplacians
Bonheure, Denis
INFINITY LAPLACIAN
NONLINEAR EIGENVALUE PROBLEM
P-LAPLACIAN
VISCOSITY SOLUTIONS
title_short The limit as p→ ∞ in the eigenvalue problem for a system of p-Laplacians
title_full The limit as p→ ∞ in the eigenvalue problem for a system of p-Laplacians
title_fullStr The limit as p→ ∞ in the eigenvalue problem for a system of p-Laplacians
title_full_unstemmed The limit as p→ ∞ in the eigenvalue problem for a system of p-Laplacians
title_sort The limit as p→ ∞ in the eigenvalue problem for a system of p-Laplacians
dc.creator.none.fl_str_mv Bonheure, Denis
Rossi, Julio Daniel
Saintier, Nicolas Bernard Claude
author Bonheure, Denis
author_facet Bonheure, Denis
Rossi, Julio Daniel
Saintier, Nicolas Bernard Claude
author_role author
author2 Rossi, Julio Daniel
Saintier, Nicolas Bernard Claude
author2_role author
author
dc.subject.none.fl_str_mv INFINITY LAPLACIAN
NONLINEAR EIGENVALUE PROBLEM
P-LAPLACIAN
VISCOSITY SOLUTIONS
topic INFINITY LAPLACIAN
NONLINEAR EIGENVALUE PROBLEM
P-LAPLACIAN
VISCOSITY SOLUTIONS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In this paper, we study the behavior as p→ ∞ of eigenvalues and eigenfunctions of a system of p-Laplacians, that is (Formula presented.) in a bounded smooth domain Ω. Here α+ β= p. We assume that α/p→Γ and β/p→1-Γ as p→ ∞ and we prove that for the first eigenvalue λ1,p we have (λ1,p)1/p→λ∞=1/maxx∈Ωdist(x,∂Ω).Concerning the eigenfunctions (up, vp) associated with λ1,p normalized by ∫Ω|up|α|vp|β=1, there is a uniform limit (u∞, v∞) that is a solution to a limit minimization problem as well as a viscosity solution to (Formula presented.) In addition, we also analyze the limit PDE when we consider higher eigenvalues.
Fil: Bonheure, Denis. Université Libre de Bruxelles; Bélgica
Fil: Rossi, Julio Daniel. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Saintier, Nicolas Bernard Claude. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description In this paper, we study the behavior as p→ ∞ of eigenvalues and eigenfunctions of a system of p-Laplacians, that is (Formula presented.) in a bounded smooth domain Ω. Here α+ β= p. We assume that α/p→Γ and β/p→1-Γ as p→ ∞ and we prove that for the first eigenvalue λ1,p we have (λ1,p)1/p→λ∞=1/maxx∈Ωdist(x,∂Ω).Concerning the eigenfunctions (up, vp) associated with λ1,p normalized by ∫Ω|up|α|vp|β=1, there is a uniform limit (u∞, v∞) that is a solution to a limit minimization problem as well as a viscosity solution to (Formula presented.) In addition, we also analyze the limit PDE when we consider higher eigenvalues.
publishDate 2016
dc.date.none.fl_str_mv 2016-10
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/11336/59873
Bonheure, Denis; Rossi, Julio Daniel; Saintier, Nicolas Bernard Claude; The limit as p→ ∞ in the eigenvalue problem for a system of p-Laplacians; Springer Heidelberg; Annali Di Matematica Pura Ed Applicata; 195; 5; 10-2016; 1771-1785
0373-3114
1618-1891
CONICET Digital
CONICET
url http://hdl.handle.net/11336/59873
identifier_str_mv Bonheure, Denis; Rossi, Julio Daniel; Saintier, Nicolas Bernard Claude; The limit as p→ ∞ in the eigenvalue problem for a system of p-Laplacians; Springer Heidelberg; Annali Di Matematica Pura Ed Applicata; 195; 5; 10-2016; 1771-1785
0373-3114
1618-1891
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1007/s10231-015-0547-2
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s10231-015-0547-2
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
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
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score 13.13397

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