WIAS Preprint No. 1944, (2014)
All functions are locally s-harmonic up to a small error
- Dipierro, Serena
- Savin, Ovidiu
- Valdinoci, Enrico
2010 Mathematics Subject Classification
- 35R11 60G22 35A35 34A08
- Density properties, approximation, s-harmonic functions
We show that we can approximate locally every function with a fractional harmonic function in that vanishes outside a compact set. 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.
- J. Eur. Math. Soc. (JEMS), 19 (2017) pp. 957-966.