The limit as p → + ∞ of the first eigenvalue for the p-Laplacian with mixed Dirichlet and Robin boundary conditions

We analyze the behavior as p→∞ of the first eigenvalue of the p-Laplacian with mixed boundary conditions of Dirichlet-Robin type. We find a nontrivial limit that we associate to a variational principle involving L∞-norms. Moreover, we provide a geometrical characterization of the limit value as well...

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Detalles Bibliográficos
Autor principal: Rossi, Julio Daniel
Publicado: 2015
Materias:
Eigenvalue problems
First variations
Infinity Laplacian
Boundary conditions
Laplace transforms
Mass transportation
Variational techniques
Eigen-value
Eigenvalue problem
Infinity laplacian
Limit values
Mixed boundary condition
Robin boundary conditions
Variational principles
Eigenvalues and eigenfunctions
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0362546X_v119_n_p167_Rossi
http://hdl.handle.net/20.500.12110/paper_0362546X_v119_n_p167_Rossi
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling paper:paper_0362546X_v119_n_p167_Rossi2023-06-08T15:35:13Z The limit as p → + ∞ of the first eigenvalue for the p-Laplacian with mixed Dirichlet and Robin boundary conditions Rossi, Julio Daniel Eigenvalue problems First variations Infinity Laplacian Boundary conditions Laplace transforms Mass transportation Variational techniques Eigen-value Eigenvalue problem First variations Infinity laplacian Limit values Mixed boundary condition Robin boundary conditions Variational principles Eigenvalues and eigenfunctions We analyze the behavior as p→∞ of the first eigenvalue of the p-Laplacian with mixed boundary conditions of Dirichlet-Robin type. We find a nontrivial limit that we associate to a variational principle involving L∞-norms. Moreover, we provide a geometrical characterization of the limit value as well as a description of it using optimal mass transportation techniques. Our results interpolate between the pure Dirichlet case and the mixed Dirichlet-Neumann case. © 2014 Elsevier Ltd. All rights reserved. Fil:Rossi, J.D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2015 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0362546X_v119_n_p167_Rossi http://hdl.handle.net/20.500.12110/paper_0362546X_v119_n_p167_Rossi
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Eigenvalue problems
First variations
Infinity Laplacian
Boundary conditions
Laplace transforms
Mass transportation
Variational techniques
Eigen-value
Eigenvalue problem
First variations
Infinity laplacian
Limit values
Mixed boundary condition
Robin boundary conditions
Variational principles
Eigenvalues and eigenfunctions
spellingShingle Eigenvalue problems
First variations
Infinity Laplacian
Boundary conditions
Laplace transforms
Mass transportation
Variational techniques
Eigen-value
Eigenvalue problem
First variations
Infinity laplacian
Limit values
Mixed boundary condition
Robin boundary conditions
Variational principles
Eigenvalues and eigenfunctions
Rossi, Julio Daniel
The limit as p → + ∞ of the first eigenvalue for the p-Laplacian with mixed Dirichlet and Robin boundary conditions
topic_facet Eigenvalue problems
First variations
Infinity Laplacian
Boundary conditions
Laplace transforms
Mass transportation
Variational techniques
Eigen-value
Eigenvalue problem
First variations
Infinity laplacian
Limit values
Mixed boundary condition
Robin boundary conditions
Variational principles
Eigenvalues and eigenfunctions
description We analyze the behavior as p→∞ of the first eigenvalue of the p-Laplacian with mixed boundary conditions of Dirichlet-Robin type. We find a nontrivial limit that we associate to a variational principle involving L∞-norms. Moreover, we provide a geometrical characterization of the limit value as well as a description of it using optimal mass transportation techniques. Our results interpolate between the pure Dirichlet case and the mixed Dirichlet-Neumann case. © 2014 Elsevier Ltd. All rights reserved.
author Rossi, Julio Daniel
author_facet Rossi, Julio Daniel
author_sort Rossi, Julio Daniel
title The limit as p → + ∞ of the first eigenvalue for the p-Laplacian with mixed Dirichlet and Robin boundary conditions
title_short The limit as p → + ∞ of the first eigenvalue for the p-Laplacian with mixed Dirichlet and Robin boundary conditions
title_full The limit as p → + ∞ of the first eigenvalue for the p-Laplacian with mixed Dirichlet and Robin boundary conditions
title_fullStr The limit as p → + ∞ of the first eigenvalue for the p-Laplacian with mixed Dirichlet and Robin boundary conditions
title_full_unstemmed The limit as p → + ∞ of the first eigenvalue for the p-Laplacian with mixed Dirichlet and Robin boundary conditions
title_sort limit as p → + ∞ of the first eigenvalue for the p-laplacian with mixed dirichlet and robin boundary conditions
publishDate 2015
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0362546X_v119_n_p167_Rossi
http://hdl.handle.net/20.500.12110/paper_0362546X_v119_n_p167_Rossi
work_keys_str_mv AT rossijuliodaniel thelimitaspofthefirsteigenvaluefortheplaplacianwithmixeddirichletandrobinboundaryconditions
AT rossijuliodaniel limitaspofthefirsteigenvaluefortheplaplacianwithmixeddirichletandrobinboundaryconditions
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