Local approximation of arbitrary functions by solutions of nonlocal equations

Serena Dipierro, Ovidiu Savin, Enrico Valdinoci

Published 2016-09-14Version 1

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.