  We establish sharp energy estimates for some solutions, such as global
minimizers, monotone solutions and saddle-shaped solutions, of the fractional
nonlinear equation $(-\Delta)^{1/2} u=f(u)$ in $\re^n$. Our energy estimates
hold for every nonlinearity $f$ and are sharp since they are optimal for
one-dimensional solutions, that is, for solutions depending only on one
Euclidian variable. As a consequence, in dimension $n=3$, we deduce the
one-dimensional symmetry of every global minimizer and of every monotone
solution. This result is the analog of a conjecture of De Giorgi on
one-dimensional symmetry for the classical equation $-\Delta u=f(u)$ in
$\re^n$.
