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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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_16642368_v6_n4_p365_DelPezzo |
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todo:paper_16642368_v6_n4_p365_DelPezzo2023-10-03T16:29:04Z The first eigenvalue of the p- Laplacian on quantum graphs Del Pezzo, L.M. Rossi, J.D. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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, L.M. Rossi, J.D. 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. |
| format |
JOUR |
| author |
Del Pezzo, L.M. Rossi, J.D. |
| author_facet |
Del Pezzo, L.M. Rossi, J.D. |
| author_sort |
Del Pezzo, L.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 |
| url |
http://hdl.handle.net/20.500.12110/paper_16642368_v6_n4_p365_DelPezzo |
| work_keys_str_mv |
AT delpezzolm thefirsteigenvalueoftheplaplacianonquantumgraphs AT rossijd thefirsteigenvalueoftheplaplacianonquantumgraphs AT delpezzolm firsteigenvalueoftheplaplacianonquantumgraphs AT rossijd firsteigenvalueoftheplaplacianonquantumgraphs |
| _version_ |
1807317078972039168 |