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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
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
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
Volumen:119
Página de inicio:167
Página de fin:178
DOI: http://dx.doi.org/10.1016/j.na.2014.09.005
Título revista:Nonlinear Analysis, Theory, Methods and Applications
Título revista abreviado:Nonlinear Anal Theory Methods Appl
ISSN:0362546X
CODEN:NOAND
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