All functions are locally -harmonic up to a small error
Serena Dipierro
University of Melbourne, Parkville, AustraliaOvidiu Savin
Columbia University, New York, USAEnrico Valdinoci
University of Melbourne, Australia, University of Milano, Italy, and WIAS, Berlin, Germany
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Abstract
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