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Abstract:

We deal with the first eigenvalue for a system of two p-Laplacians with Dirichlet and Neumann boundary conditions. If Δpw = div (|∇w|p-2∇w) stands for the p-Laplacian and α/p + β/q = 1, we consider (Formula presented.) with mixed boundary conditions (Formula presented.) We show that there is a first non trivial eigenvalue that can be characterized by the variational minimization problem (Formula presented.), where (Formula presented.). We also study the limit of λ α,β p,q, as q,p → ∞ assuming that α/p → F ∈ (0, 1), and q/p → Q ∈ (0, ∞) as p,q → ∞. We find that this limit problem interpolates between the pure Dirichlet and Neumann cases for a single equation when we take Q = 1 and the limits F → 1 and F → 0. © 2015 Elsevier Ltd. All rights reserved.

Registro:

Documento: Artículo
Título:The first nontrivial eigenvalue for a system of p-Laplacians with Neumann and Dirichlet boundary conditions
Autor:Del Pezzo, L.M.; Rossi, J.D.
Filiación:CONICET, Departamento de Matemática, FCEyN, Universidad de Buenos Aires, Ciudad Universitaria, Pabellon i, Buenos Aires, 1428, Argentina
Palabras clave:Eigenvalues; p-Laplacian; Systems; Computer systems; Eigenvalues and eigenfunctions; Laplace equation; Laplace transforms; Dirichlet and Neumann boundary conditions; Eigenvalues; Limit problem; Minimization problems; Mixed boundary condition; Neumann and Dirichlet boundary conditions; P-Laplacian; Single equation; Boundary conditions
Año:2016
Volumen:137
Página de inicio:381
Página de fin:401
DOI: http://dx.doi.org/10.1016/j.na.2015.09.019
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_v137_n_p381_DelPezzo

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Citas:

---------- APA ----------
Del Pezzo, L.M. & Rossi, J.D. (2016) . The first nontrivial eigenvalue for a system of p-Laplacians with Neumann and Dirichlet boundary conditions. Nonlinear Analysis, Theory, Methods and Applications, 137, 381-401.
http://dx.doi.org/10.1016/j.na.2015.09.019
---------- CHICAGO ----------
Del Pezzo, L.M., Rossi, J.D. "The first nontrivial eigenvalue for a system of p-Laplacians with Neumann and Dirichlet boundary conditions" . Nonlinear Analysis, Theory, Methods and Applications 137 (2016) : 381-401.
http://dx.doi.org/10.1016/j.na.2015.09.019
---------- MLA ----------
Del Pezzo, L.M., Rossi, J.D. "The first nontrivial eigenvalue for a system of p-Laplacians with Neumann and Dirichlet boundary conditions" . Nonlinear Analysis, Theory, Methods and Applications, vol. 137, 2016, pp. 381-401.
http://dx.doi.org/10.1016/j.na.2015.09.019
---------- VANCOUVER ----------
Del Pezzo, L.M., Rossi, J.D. The first nontrivial eigenvalue for a system of p-Laplacians with Neumann and Dirichlet boundary conditions. Nonlinear Anal Theory Methods Appl. 2016;137:381-401.
http://dx.doi.org/10.1016/j.na.2015.09.019