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http://www.repositorio.ufop.br/jspui/handle/123456789/9261
Title: | Asymptotic behavior of the p-torsion functions as p goes to 1. |
Authors: | Bueno, Hamilton Prado Ercole, Grey Macedo, Shirley da Silva |
Keywords: | Asymptotic behavior Cheeger constant |
Issue Date: | 2016 |
Citation: | BUENO, H. P.; 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. |
Abstract: | Let 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. |
URI: | http://www.repositorio.ufop.br/handle/123456789/9261 |
metadata.dc.identifier.uri2: | https://link.springer.com/article/10.1007/s00013-016-0922-2 |
metadata.dc.identifier.doi: | https://doi.org/10.1007/s00013-016-0922-2 |
ISSN: | 1420-8938 |
Appears in Collections: | DECEA - Artigos publicados em periódicos |
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ARTIGO_AsymptoticBehaviorPtorsion.pdf Restricted Access | 521,97 kB | Adobe PDF | View/Open |
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