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Abstract:

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.

Registro:

Documento: Artículo
Título:The first eigenvalue of the p- Laplacian on quantum graphs
Autor:Del Pezzo, L.M.; Rossi, J.D.
Filiación:CONICET and Departamento de Matemática, FCEyN, Universidad de Buenos Aires, Pabellon I, Ciudad Universitaria (1428), Buenos Aires, Argentina
Palabras clave:Eigenvalues; p- Laplacian; Quantum graphs; Shape derivative
Año:2016
Volumen:6
Número:4
Página de inicio:365
Página de fin:391
DOI: http://dx.doi.org/10.1007/s13324-016-0123-y
Título revista:Analysis and Mathematical Physics
Título revista abreviado:Anal. Math. Phys.
ISSN:16642368
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_16642368_v6_n4_p365_DelPezzo

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Citas:

---------- APA ----------
Del Pezzo, L.M. & Rossi, J.D. (2016) . The first eigenvalue of the p- Laplacian on quantum graphs. Analysis and Mathematical Physics, 6(4), 365-391.
http://dx.doi.org/10.1007/s13324-016-0123-y
---------- CHICAGO ----------
Del Pezzo, L.M., Rossi, J.D. "The first eigenvalue of the p- Laplacian on quantum graphs" . Analysis and Mathematical Physics 6, no. 4 (2016) : 365-391.
http://dx.doi.org/10.1007/s13324-016-0123-y
---------- MLA ----------
Del Pezzo, L.M., Rossi, J.D. "The first eigenvalue of the p- Laplacian on quantum graphs" . Analysis and Mathematical Physics, vol. 6, no. 4, 2016, pp. 365-391.
http://dx.doi.org/10.1007/s13324-016-0123-y
---------- VANCOUVER ----------
Del Pezzo, L.M., Rossi, J.D. The first eigenvalue of the p- Laplacian on quantum graphs. Anal. Math. Phys. 2016;6(4):365-391.
http://dx.doi.org/10.1007/s13324-016-0123-y