preprint

Inserted: 19 oct 2025
Last Updated: 19 oct 2025

Year: 2025

Abstract:

For $s\in(0,1)$ and an open bounded set $\Omega\subset\mathbb R^n$, we prove existence and uniqueness of absolute minimisers of the $L^\infty$-norm of the Fractional Laplacian in $\mathbb{R}^n$, with prescribed Dirichlet data in the complement of $\Omega$. We further show that the minimiser $u_\infty$ satisfies a particular (fractional) PDE in $\Omega$.