Fractional Laplacian: Pohozaev identity and nonexistence results
  In this note we present the Pohozaev identity for the fractional Laplacian. As a consequence of this identity, we prove the nonexistence of nontrivial bounded solutions to semilinear problems with supercritical nonlinearities in star-shaped domains. 
Xavier Ros-Oton, Joaquim Serra
math.AP