WIAS Preprint No. 2303, (2016)

Local approximation of arbitrary functions by solutions of nonlocal equations



Authors

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

2010 Mathematics Subject Classification

  • 35R11 60G22 35A35 34A08

Keywords

  • density properties, approximation, s-caloric functions

Abstract

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.

Appeared in

  • J. Geom. Anal. (2018), https://doi.org/10.1007/s12220-018-0045-z.

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