The first eigenvalue of the p- Laplacian on quantum graphs

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...

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Autores principales: Del Pezzo, Leandro M., Rossi, Julio Daniel
Publicado: 2016
Materias:
Eigenvalues
p- Laplacian
Quantum graphs
Shape derivative
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_16642368_v6_n4_p365_DelPezzo
http://hdl.handle.net/20.500.12110/paper_16642368_v6_n4_p365_DelPezzo
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_16642368_v6_n4_p365_DelPezzo
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spelling paper:paper_16642368_v6_n4_p365_DelPezzo2023-06-08T16:26:01Z The first eigenvalue of the p- Laplacian on quantum graphs Del Pezzo, Leandro M. Rossi, Julio Daniel Eigenvalues p- Laplacian Quantum graphs Shape derivative 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. © 2016, Springer International Publishing. Fil:Del Pezzo, L.M. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Rossi, J.D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2016 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_16642368_v6_n4_p365_DelPezzo http://hdl.handle.net/20.500.12110/paper_16642368_v6_n4_p365_DelPezzo
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Eigenvalues
p- Laplacian
Quantum graphs
Shape derivative
spellingShingle Eigenvalues
p- Laplacian
Quantum graphs
Shape derivative
Del Pezzo, Leandro M.
Rossi, Julio Daniel
The first eigenvalue of the p- Laplacian on quantum graphs
topic_facet Eigenvalues
p- Laplacian
Quantum graphs
Shape derivative
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. © 2016, Springer International Publishing.
author Del Pezzo, Leandro M.
Rossi, Julio Daniel
author_facet Del Pezzo, Leandro M.
Rossi, Julio Daniel
author_sort Del Pezzo, Leandro M.
title The first eigenvalue of the p- Laplacian on quantum graphs
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 first eigenvalue of the p- laplacian on quantum graphs
publishDate 2016
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_16642368_v6_n4_p365_DelPezzo
http://hdl.handle.net/20.500.12110/paper_16642368_v6_n4_p365_DelPezzo
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