  Our concern is the computation of optimal shapes in problems involving
$\(-\Delta)^{1/2}$. We focus on the energy $J(\Omega)$ associated to the
solution $u\_\Omega$ of the basic Dirichlet problem $(-\Delta)^{1/2} u\_\Omega
= 1$ in $\Omega$, $ u = 0$ in $\Omega^c$. We show that regular minimizers
$\Omega$ of this energy under a volume constraint are disks. Our proof goes
through the explicit computation of the shape derivative (that seems to be
completely new in the fractional context), and a refined adaptation of the
moving plane method.
