WIAS Preprint No. 1944, (2014)

All functions are locally s-harmonic up to a small error


  • Dipierro, Serena
  • Savin, Ovidiu
  • Valdinoci, Enrico
    ORCID: 0000-0001-6222-2272

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.

Appeared in

  • J. Eur. Math. Soc. (JEMS), 19 (2017) pp. 957-966.

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