Abstract:
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.
Registro:
Documento: |
Artículo
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Título: | The limit as p → + ∞ of the first eigenvalue for the p-Laplacian with mixed Dirichlet and Robin boundary conditions |
Autor: | Rossi, J.D.; Saintier, N. |
Filiación: | Departamento de Matemática, FCEyN, Univ. de Buenos Aires, C.P. 1428, Buenos Aires, Argentina Instituto de Ciencias, Univ. Gral Sarmiento, Juan María Gutierrez 1150, Los Polvorines, Pcia de Buenos Aires, Argentina
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Palabras clave: | 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 |
Año: | 2015
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Volumen: | 119
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Página de inicio: | 167
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Página de fin: | 178
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DOI: |
http://dx.doi.org/10.1016/j.na.2014.09.005 |
Título revista: | Nonlinear Analysis, Theory, Methods and Applications
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Título revista abreviado: | Nonlinear Anal Theory Methods Appl
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ISSN: | 0362546X
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CODEN: | NOAND
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Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0362546X_v119_n_p167_Rossi |
Referencias:
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Citas:
---------- APA ----------
Rossi, J.D. & Saintier, N.
(2015)
. The limit as p → + ∞ of the first eigenvalue for the p-Laplacian with mixed Dirichlet and Robin boundary conditions. Nonlinear Analysis, Theory, Methods and Applications, 119, 167-178.
http://dx.doi.org/10.1016/j.na.2014.09.005---------- CHICAGO ----------
Rossi, J.D., Saintier, N.
"The limit as p → + ∞ of the first eigenvalue for the p-Laplacian with mixed Dirichlet and Robin boundary conditions"
. Nonlinear Analysis, Theory, Methods and Applications 119
(2015) : 167-178.
http://dx.doi.org/10.1016/j.na.2014.09.005---------- MLA ----------
Rossi, J.D., Saintier, N.
"The limit as p → + ∞ of the first eigenvalue for the p-Laplacian with mixed Dirichlet and Robin boundary conditions"
. Nonlinear Analysis, Theory, Methods and Applications, vol. 119, 2015, pp. 167-178.
http://dx.doi.org/10.1016/j.na.2014.09.005---------- VANCOUVER ----------
Rossi, J.D., Saintier, N. The limit as p → + ∞ of the first eigenvalue for the p-Laplacian with mixed Dirichlet and Robin boundary conditions. Nonlinear Anal Theory Methods Appl. 2015;119:167-178.
http://dx.doi.org/10.1016/j.na.2014.09.005