Superharmonicity of the fractional ground state

We prove that the positive ground state $u$ of the fractional Laplacian $(-Δ)^s$, $s\in (0,1)$, on an arbitrary open set $Ω$ satisfies $-Δu>λ_s(Ω)^{1/s}u$ in $Ω$. In one dimension, this yields strong concavity and settles a conjecture of Bañuelos, Kulczycki, and Méndez-Hernández. We establish a hier