This paper concerns the study of the asymptotic behavior of the solutions to a family of fractional type problems on a bounded domain, satisfying homogeneous Dirichlet boundary conditions. The family of differential operators includes the fractional \(p_n\)-Laplacian when \(p_n\rightarrow \infty \) as a particular case, tough it could be extended to a function of the Hölder quotient of order s, whose primitive is an Orlicz function satisfying appropriated growth conditions. The limit equation involves the Hölder infinity Laplacian.

中文翻译：

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作为Orlicz分式拉普拉斯算子的极限而获得的Hölder无限拉普拉斯算子

本文涉及满足齐次Dirichlet边界条件的有界域上一类分数型问题解的渐近行为的研究。微分算子家族包括分数\（p_n \）- Laplacian，当\（p_n \ rightarrow \ infty \）在特定情况下，很难将其扩展为阶s的Hölder商的函数，该商的原语是Orlicz函数满足适当的生长条件。极限方程涉及Hölder无限拉普拉斯算子。