Torsion functions and the Cheeger problem : a fractional approach.

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MetadadosDescriçãoIdioma
Autor(es): dc.creatorBueno, Hamilton Prado-
Autor(es): dc.creatorErcole, Grey-
Autor(es): dc.creatorMacedo, Shirley da Silva-
Autor(es): dc.creatorPereira, Gilberto A.-
Data de aceite: dc.date.accessioned2025-08-21T15:04:39Z-
Data de disponibilização: dc.date.available2025-08-21T15:04:39Z-
Data de envio: dc.date.issued2018-04-16-
Data de envio: dc.date.issued2018-04-16-
Data de envio: dc.date.issued2016-
Fonte completa do material: dc.identifierhttp://www.repositorio.ufop.br/handle/123456789/9844-
Fonte completa do material: dc.identifierhttps://www.degruyter.com/view/j/ans.2016.16.issue-4/ans-2015-5048/ans-2015-5048.xml-
Fonte completa do material: dc.identifierhttps://doi.org/10.1515/ans-2015-5048-
Fonte: dc.identifier.urihttp://educapes.capes.gov.br/handle/capes/1002009-
Descrição: dc.descriptionLet Ω be a Lipschitz bounded domain of ℝN, N ≥ 2. The fractional Cheeger constant hs(Ω), 0 < s < 1, is defined by hs(Ω) = inf E⊂Ω Ps(E) |E| , where Ps(E) = ∫ ℝN ∫ ℝN |χE(x) − χE(y)| |x − y| N+s dx dy, with χE denoting the characteristic function of the smooth subdomain E. The main purpose of this paper is to show that lim p→1 + |ϕ s p | 1−p L∞(Ω) = hs(Ω) = lim p→1 + |ϕ s p | 1−p L 1(Ω) , where ϕ s p is the fractional (s, p)-torsion function of Ω, that is, the solution of the Dirichlet problem for the fractional p-Laplacian: −(∆) s p u = 1 in Ω, u = 0 in ℝN \ Ω. For this, we derive suitable bounds for the first eigenvalue λ s 1,p (Ω) of the fractional p-Laplacian operator in terms of ϕ s p . We also show that ϕ s p minimizes the (s, p)-Gagliardo seminorm in ℝN, among the functions normalized by the L 1 -norm.-
Formato: dc.formatapplication/pdf-
Idioma: dc.languagept_BR-
Direitos: dc.rightsrestrito-
Palavras-chave: dc.subjectFractional cheeger problem-
Palavras-chave: dc.subjectTorsion functions-
Palavras-chave: dc.subjectFractional-
Palavras-chave: dc.subjectFractional p-Laplacian-
Título: dc.titleTorsion functions and the Cheeger problem : a fractional approach.-
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