The first nontrivial eigenvalue for a system of p-Laplacians with Neumann and Dirichlet boundary conditions
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...
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todo:paper_0362546X_v137_n_p381_DelPezzo2023-10-03T15:27:10Z The first nontrivial eigenvalue for a system of p-Laplacians with Neumann and Dirichlet boundary conditions Del Pezzo, L.M. Rossi, J.D. 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 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. Fil:Del Pezzo, L.M. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Rossi, J.D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_0362546X_v137_n_p381_DelPezzo |
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Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
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 |
| spellingShingle |
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 Del Pezzo, L.M. Rossi, J.D. The first nontrivial eigenvalue for a system of p-Laplacians with Neumann and Dirichlet boundary conditions |
| topic_facet |
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 |
| description |
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. |
| format |
JOUR |
| author |
Del Pezzo, L.M. Rossi, J.D. |
| author_facet |
Del Pezzo, L.M. Rossi, J.D. |
| author_sort |
Del Pezzo, L.M. |
| title |
The first nontrivial eigenvalue for a system of p-Laplacians with Neumann and Dirichlet boundary conditions |
| title_short |
The first nontrivial eigenvalue for a system of p-Laplacians with Neumann and Dirichlet boundary conditions |
| title_full |
The first nontrivial eigenvalue for a system of p-Laplacians with Neumann and Dirichlet boundary conditions |
| title_fullStr |
The first nontrivial eigenvalue for a system of p-Laplacians with Neumann and Dirichlet boundary conditions |
| title_full_unstemmed |
The first nontrivial eigenvalue for a system of p-Laplacians with Neumann and Dirichlet boundary conditions |
| title_sort |
first nontrivial eigenvalue for a system of p-laplacians with neumann and dirichlet boundary conditions |
| url |
http://hdl.handle.net/20.500.12110/paper_0362546X_v137_n_p381_DelPezzo |
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