Raffaella Servadei and Enrico Valdinoci
Weak and viscosity solutions
of the fractional Laplace equation
(40K, LaTeX)

ABSTRACT.  Aim of this paper is to show that weak solutions of the
following fractional Laplacian equation $$\left\{ egin{matrix}
(-\Delta)^s u=f & {\mbox{ in }}\Omega,\ u=g &{\mbox{ in
}}\RR^n\setminus\Omega \end{matrix}
ight.  $$ are also continuous
solutions of this problem in the viscosity sense.