The first eigenvalue of the p- Laplacian on quantum graphs

Autores
del Pezzo, Leandro Martin; Rossi, Julio Daniel
Año de publicación
2016
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We study the first eigenvalue of the p- Laplacian (with 1 < p< ∞) on a quantum graph with Dirichlet or Kirchoff boundary conditions on the nodes. We find lower and upper bounds for this eigenvalue when we prescribe the total sum of the lengths of the edges and the number of Dirichlet nodes of the graph. Also we find a formula for the shape derivative of the first eigenvalue (assuming that it is simple) when we perturb the graph by changing the length of an edge. Finally, we study in detail the limit cases p→ ∞ and p→ 1.
Fil: del Pezzo, Leandro Martin. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
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
Materia
Eigenvalues
P- Laplacian
Quantum Graphs
Shape Derivative
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:11336/59802
Acceder
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network_name_str CONICET Digital (CONICET)
spelling The first eigenvalue of the p- Laplacian on quantum graphsdel Pezzo, Leandro MartinRossi, Julio DanielEigenvaluesP- LaplacianQuantum GraphsShape Derivativehttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We study the first eigenvalue of the p- Laplacian (with 1 < p< ∞) on a quantum graph with Dirichlet or Kirchoff boundary conditions on the nodes. We find lower and upper bounds for this eigenvalue when we prescribe the total sum of the lengths of the edges and the number of Dirichlet nodes of the graph. Also we find a formula for the shape derivative of the first eigenvalue (assuming that it is simple) when we perturb the graph by changing the length of an edge. Finally, we study in detail the limit cases p→ ∞ and p→ 1.Fil: del Pezzo, Leandro Martin. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Rossi, Julio Daniel. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaSpringer2016-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/59802del Pezzo, Leandro Martin; Rossi, Julio Daniel; The first eigenvalue of the p- Laplacian on quantum graphs; Springer; Analysis and Mathematical Physics; 6; 4; 12-2016; 365-3911664-23681664-235XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1007/s13324-016-0123-yinfo:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs13324-016-0123-yinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:18:31Zoai:ri.conicet.gov.ar:11336/59802instacron: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 10:18:31.45CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv The first eigenvalue of the p- Laplacian on quantum graphs
title The first eigenvalue of the p- Laplacian on quantum graphs
spellingShingle The first eigenvalue of the p- Laplacian on quantum graphs
del Pezzo, Leandro Martin
Eigenvalues
P- Laplacian
Quantum Graphs
Shape Derivative
title_short The first eigenvalue of the p- Laplacian on quantum graphs
title_full The first eigenvalue of the p- Laplacian on quantum graphs
title_fullStr The first eigenvalue of the p- Laplacian on quantum graphs
title_full_unstemmed The first eigenvalue of the p- Laplacian on quantum graphs
title_sort The first eigenvalue of the p- Laplacian on quantum graphs
dc.creator.none.fl_str_mv del Pezzo, Leandro Martin
Rossi, Julio Daniel
author del Pezzo, Leandro Martin
author_facet del Pezzo, Leandro Martin
Rossi, Julio Daniel
author_role author
author2 Rossi, Julio Daniel
author2_role author
dc.subject.none.fl_str_mv Eigenvalues
P- Laplacian
Quantum Graphs
Shape Derivative
topic Eigenvalues
P- Laplacian
Quantum Graphs
Shape Derivative
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We study the first eigenvalue of the p- Laplacian (with 1 < p< ∞) on a quantum graph with Dirichlet or Kirchoff boundary conditions on the nodes. We find lower and upper bounds for this eigenvalue when we prescribe the total sum of the lengths of the edges and the number of Dirichlet nodes of the graph. Also we find a formula for the shape derivative of the first eigenvalue (assuming that it is simple) when we perturb the graph by changing the length of an edge. Finally, we study in detail the limit cases p→ ∞ and p→ 1.
Fil: del Pezzo, Leandro Martin. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
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
description We study the first eigenvalue of the p- Laplacian (with 1 < p< ∞) on a quantum graph with Dirichlet or Kirchoff boundary conditions on the nodes. We find lower and upper bounds for this eigenvalue when we prescribe the total sum of the lengths of the edges and the number of Dirichlet nodes of the graph. Also we find a formula for the shape derivative of the first eigenvalue (assuming that it is simple) when we perturb the graph by changing the length of an edge. Finally, we study in detail the limit cases p→ ∞ and p→ 1.
publishDate 2016
dc.date.none.fl_str_mv 2016-12
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/11336/59802
del Pezzo, Leandro Martin; Rossi, Julio Daniel; The first eigenvalue of the p- Laplacian on quantum graphs; Springer; Analysis and Mathematical Physics; 6; 4; 12-2016; 365-391
1664-2368
1664-235X
CONICET Digital
CONICET
url http://hdl.handle.net/11336/59802
identifier_str_mv del Pezzo, Leandro Martin; Rossi, Julio Daniel; The first eigenvalue of the p- Laplacian on quantum graphs; Springer; Analysis and Mathematical Physics; 6; 4; 12-2016; 365-391
1664-2368
1664-235X
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/s13324-016-0123-y
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs13324-016-0123-y
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
publisher.none.fl_str_mv Springer
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 13.070432

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