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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| Autores principales: | , |
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| Formato: | JOUR |
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_0362546X_v137_n_p381_DelPezzo |
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| Sumario: | 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. |
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