Local approximation of arbitrary functions by solutions of nonlocal equations
- Dipierro, Serena
- Savin, Ovidiu
- Valdinoci, Enrico
2010 Mathematics Subject Classification
- 35R11 60G22 35A35 34A08
- density properties, approximation, s-caloric functions
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.
- J. Geom. Anal. (2018), https://doi.org/10.1007/s12220-018-0045-z.