Accepted Paper

Inserted: 19 oct 2025
Last Updated: 7 jun 2026

Journal: Nonlinear Analysis
Year: 2026

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 $\Omega$.

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• CM_preprint.pdf