All functions are locally -harmonic up to a small error

  • Serena Dipierro

    University of Melbourne, Parkville, Australia
  • Ovidiu Savin

    Columbia University, New York, USA
  • Enrico Valdinoci

    University of Melbourne, Australia, University of Milano, Italy, and WIAS, Berlin, Germany


We show that we can approximate every function by an -harmonic function in that vanishes outside a compact set.

That is, -harmonic functions are dense in .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.

Cite this article

Serena Dipierro, Ovidiu Savin, Enrico Valdinoci, All functions are locally -harmonic up to a small error. J. Eur. Math. Soc. 19 (2017), no. 4, pp. 957–966

DOI 10.4171/JEMS/684