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Title: Computing the first eigenpair of the p-Laplacian in annuli.
Authors: Ercole, Grey
Espírito Santo, Júlio César do
Martins, Eder Marinho
Keywords: Annulus
First eigenpair
Inverse iteration method
Issue Date: 2015
Citation: ERCOLE, G.; ESPÍRITO SANTO, J. C. do.; MARTINS, E. M. Computing the first eigenpair of the p-Laplacian in annuli. Journal of Mathematical Analysis and Applications, v. 422, p. 1277-1307, 2015. Disponível em: <>. Acesso em: 23 mar. 2017.
Abstract: We propose a method for computing the first eigenpair of the Dirichlet p-Laplacian, p > 1, in the annulus Ωa,b = {x ∈ RN : a < |x| < b}, N > 1. For each t ∈ (a, b), we use an inverse iteration method to solve two radial eigenvalue problems: one in the annulus Ωa,t, with the corresponding eigenvalue λ−(t) and boundary conditions u(a) = 0 = u (t); and the other in the annulus Ωt,b, with the corresponding eigenvalue λ+(t) and boundary conditions u (t) = 0 = u(b). Next, we adjust the parameter t using a matching procedure to make λ−(t) coincide with λ+(t), thereby obtaining the first eigenvalue λp. Hence, by a simple splicing argument, we obtain the positive, L∞-normalized, radial first eigenfunction up. The matching parameter is the maximum point ρ of up. In order to apply this method, we derive estimates for λ−(t) and λ+(t), and we prove that these functions are monotone and (locally Lipschitz) continuous. Moreover, we derive upper and lower estimates for the maximum point ρ, which we use in the matching procedure, and we also present a direct proof that up converges to the L∞-normalized distance function to the boundary as p → ∞. We also present some numerical results obtained using this method.
ISSN: 0022-247X
metadata.dc.rights.license: O periódico Journal of Mathematical Analysis and Applications concede permissão para depósito deste artigo no Repositório Institucional da UFOP. Número da licença: 4073071202962.
Appears in Collections:DEMAT - Artigos publicados em periódicos

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