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10.3233-ASY-211702 |
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220425s2022 CNT 000 0 und d |
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|a 09217134 (ISSN)
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|a A system of local/nonlocal p-Laplacians: The eigenvalue problem and its asymptotic limit as p → ∞
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|b IOS Press BV
|c 2022
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|z View Fulltext in Publisher
|u https://doi.org/10.3233/ASY-211702
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|a In this work, given p ϵ (1, ∞), we prove the existence and simplicity of the first eigenvalue λ p and its corresponding eigenvector (u p, v p), for the following local/nonlocal PDE system (0.1)-δ p u + (-δ) p r u = 2 α α + β λ | u | α-2 | v | β u in ω-δ p v + (-δ) p s v = 2 β α + β λ | u | α | v | β-2 v in ω u = 0 on R N-ω v = 0 on R N-ω, where ω R N is a bounded open domain, 0 < r, s < 1 and α (p) + β (p) = p. Moreover, we address the asymptotic limit as p → ∞, proving the explicit geometric characterization of the corresponding first ∞-eigenvalue, namely λ ∞, and the uniformly convergence of the pair (u p, v p) to the ∞-eigenvector (u ∞, v ∞). Finally, the triple (u ∞, v ∞, λ ∞) verifies, in the viscosity sense, a limiting PDE system. © 2022-IOS Press. All rights reserved.
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|a Asymptotic analysis
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|a Asymptotic limits
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|a Eigenvalue problem
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|a Eigenvalues and eigenfunctions
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|a First eigenvalue problem
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|a First eigenvalue problem
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|a Geometry
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|a Holder ∞-laplacian and ∞-laplacian
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|a Hölder ∞-Laplacian and ∞-Laplacian
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|a Laplace transforms
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|a Laplacians
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|a Local/nonlocal p-laplacians
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|a Local/nonlocal p-Laplacians
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|a Nonlocal
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|a Simplicity
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|a Simplicity
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|a Buccheri, S.
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|a Da Silva, J.V.
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|a De Miranda, L.H.
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|t Asymptotic Analysis
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