ALL FUNCTIONS ARE LOCALLY S-HARMONIC (UP TO A SMALL ERROR)

ALL FUNCTIONS ARE LOCALLY S-HARMONIC (UP TO A SMALL ERROR) We show that we can approximate every C^k function with a s-harmonic function in a ball that vanishes outside a compact set. That is, s-harmonic functions are locally dense in C^k. This result is clearly in contrast with the rigidity of harmonic functions in the classical case and can be viewed as a purely nonlocal feature. This is a joint work with O. Savin and E. Valdinoci.