Bueno, HamiltonErcole, GreyMacedo, Shirley da Silva2018-01-182018-01-182016BUENO, H.; ERCOLE, G.; MACEDO, S. da S. Asymptotic behavior of the p-torsion functions as p goes to 1. Archiv der Mathematik, v. 107, p. 63-72, 2016. Disponível em: <https://link.springer.com/article/10.1007/s00013-016-0922-2>. Acesso em: 02 out. 2017.1420-8938http://www.repositorio.ufop.br/handle/123456789/9261Let Ω be a Lipschitz bounded domain of RN, N ≥ 2, and let up ∈ W1,p 0 (Ω) denote the p-torsion function of Ω, p > 1. It is observed that the value 1 for the Cheeger constant h(Ω) is threshold with respect to the asymptotic behavior of up, as p → 1+, in the following sense: when h(Ω) > 1, one has limp→1+ up L∞(Ω) = 0, and when h(Ω) < 1, one has limp→1+ up L∞(Ω) = ∞. In the case h(Ω) = 1, it is proved that lim supp→1+ up L∞(Ω) < ∞. For a radial annulus Ωa,b, with inner radius a and outer radius b, it is proved that limp→1+ up L∞(Ωa,b) = 0 when h(Ωa,b) = 1.en-USrestritoAsymptotic behaviorCheeger constantArtigo publicado em periodicohttps://link.springer.com/article/10.1007/s00013-016-0922-2https://doi.org/10.1007/s00013-016-0922-2