  This paper deals with the \emph{integral} version of the Dirichlet
homogeneous fractional Laplace equation. For this problem weighted and
fractional Sobolev a priori estimates are provided in terms of the H\"older
regularity of the data. By relying on these results, optimal order of
convergence for the standard linear finite element method is proved for
quasi-uniform as well as graded meshes. Some numerical examples are given
showing results in agreement with the theoretical predictions.
