A Dirichlet problem of the fractional Laplace equation in the bounded   Lipschitz domain
  In this paper, we study a Dirichlet problem of a fractional Laplace equation in a bounded Lipschitz domain in $ \R, n \geq 2$. Our main result is that for the given data $F \in \dot H^s(\Om^c), 0 < s<1$, we find the function which satisfies that $\De^s u =0$ in $\Om$,   $u|_{\Om^c} =F$ and $|u|_{\dot{H}^s(\R)} \leq c |F|_{\dot H^s(\Om^c)}$. Furthermore, we represent the solution with an integral operator. 
Tongkeun Chang
math.AP