A Hölder infinity Laplacian obtained as limit of Orlicz fractional Laplacians. (English) Zbl 1490.35517
Summary: 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.
MSC:
| 35R11 | Fractional partial differential equations |
| 35J25 | Boundary value problems for second-order elliptic equations |
| 35J92 | Quasilinear elliptic equations with \(p\)-Laplacian |
| 45G05 | Singular nonlinear integral equations |
| 35R09 | Integro-partial differential equations |
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