Computing the first eigenpair of the p-Laplacian in annuli.

Registro completo de metadados
MetadadosDescriçãoIdioma
Autor(es): dc.creatorErcole, Grey-
Autor(es): dc.creatorEspírito Santo, Júlio César do-
Autor(es): dc.creatorMartins, Eder Marinho-
Data de aceite: dc.date.accessioned2025-08-21T15:18:02Z-
Data de disponibilização: dc.date.available2025-08-21T15:18:02Z-
Data de envio: dc.date.issued2017-03-23-
Data de envio: dc.date.issued2017-03-23-
Data de envio: dc.date.issued2015-
Fonte completa do material: dc.identifierhttp://www.repositorio.ufop.br/handle/123456789/7439-
Fonte completa do material: dc.identifierhttps://doi.org/10.1016/j.jmaa.2014.09.016-
Fonte: dc.identifier.urihttp://educapes.capes.gov.br/handle/capes/1009625-
Descrição: dc.descriptionWe 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.-
Formato: dc.formatapplication/pdf-
Idioma: dc.languageen-
Direitos: dc.rightsaberto-
Direitos: dc.rightsO periódico Journal of Mathematical Analysis and Applications concede permissão para depósito deste artigo no Repositório Institucional da UFOP. Número da licença: 4073071202962.-
Palavras-chave: dc.subjectAnnulus-
Palavras-chave: dc.subjectFirst eigenpair-
Palavras-chave: dc.subjectInverse iteration method-
Palavras-chave: dc.subjectp-Laplacian-
Título: dc.titleComputing the first eigenpair of the p-Laplacian in annuli.-
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