Ercole, GreyPereira, Gilberto de AssisSanchis, Remy de Paiva2023-02-032023-02-032019ERCOLE, G.; PEREIRA, G. de A.; SANCHIS, R de P. Asymptotic behavior of extremals for fractional Sobolev inequalities associated with singular problems. Annali di Matematica Pura ed Applicata, v. 198, p. 2059-2079, 2019. Disponível em: <https://link.springer.com/article/10.1007/s10231-019-00854-9>. Acesso em: 06 jul. 2022.1618-1891http://www.repositorio.ufop.br/jspui/handle/123456789/16104Let be a smooth, bounded domain of RN , ω be a positive, L1-normalized function, and 0 < s < 1 < p. We study the asymptotic behavior, as p → ∞, of the pair p p, u p, where p is the best constant C in the Sobolev-type inequality C exp (log |u| p)ωdx ≤ [u] p s,p ∀ u ∈ Ws,p 0 () and u p is the positive, suitably normalized extremal function corresponding to p. We show that the limit pairs are closely related to the problem of minimizing the quotient |u|s / exp (log |u|)ωdx , where |u|s denotes the s-Hölder seminorm of a function u ∈ C0,s 0 ().en-USrestritop-LaplacianViscosity solutionArtigo publicado em periodicohttps://link.springer.com/article/10.1007/s10231-019-00854-9https://doi.org/10.1007/s10231-019-00854-9