Local approximation of arbitrary functions by solutions of nonlocal   equations
  We show that any function can be locally approximated by solutions of prescribed linear equations of nonlocal type. In particular, we show that every function is locally $s$-caloric, up to a small error. The case of non-elliptic and non-parabolic operators is taken into account as well. 
Serena Dipierro, Ovidiu Savin and Enrico Valdinoci
math.AP