Please use this identifier to cite or link to this item: http://www.repositorio.ufop.br/handle/123456789/9844
Title: Torsion functions and the Cheeger problem : a fractional approach.
Authors: Bueno, Hamilton Prado
Ercole, Grey
Macedo, Shirley da Silva
Pereira, Gilberto A.
Keywords: Fractional cheeger problem
Torsion functions
Fractional
Fractional p-Laplacian
Issue Date: 2016
Citation: BUENO, H. P. et al. Torsion functions and the Cheeger problem : a fractional approach. Advanced Nonlinear Studies, v. 16, p. 689-697, 2016. Disponível em: <https://www.degruyter.com/view/j/ans.2016.16.issue-4/ans-2015-5048/ans-2015-5048.xml>. Acesso em: 02 out. 2017.
Abstract: Let 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.
URI: http://www.repositorio.ufop.br/handle/123456789/9844
metadata.dc.identifier.uri2: https://www.degruyter.com/view/j/ans.2016.16.issue-4/ans-2015-5048/ans-2015-5048.xml
ISSN: 15361365
Appears in Collections:DECEA - Artigos publicados em periódicos

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