Strict Concavity of the Torsion Function for the Restricted Half-Laplacian in Bounded Convex Domains

Jiahuan Li, Shujun Shi

Let $D\subset {\mathbb{R}}^n$, $n\ge 2$, be a bounded convex domain, and let $u_D$ be the torsion function for the restricted half-Laplacian. We prove that $D^2{u}_D$ is negative definit…