A Hölder Infinity Laplacian obtained as limit of Orlicz Fractional Laplacians

Abstract

This paper concerns with 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 $p_n\to \infty$ 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.

arXiv comment29 pages. Submitted