The Journal of Geometric Analysis

, Volume 29, Issue 2, pp 1428–1455 | Cite as

Local Approximation of Arbitrary Functions by Solutions of Nonlocal Equations

  • Serena Dipierro
  • Ovidiu Savin
  • Enrico ValdinociEmail author


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.


Density properties Approximation s-caloric functions 

Mathematics Subject Classification

35R11 60G22 35A35 34A08 


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Copyright information

© Mathematica Josephina, Inc. 2018

Authors and Affiliations

  • Serena Dipierro
    • 1
    • 2
  • Ovidiu Savin
    • 3
  • Enrico Valdinoci
    • 1
    • 2
    • 4
    • 5
    Email author
  1. 1.Dipartimento di MatematicaUniversità degli studi di MilanoMilanItaly
  2. 2.Department of Mathematics and StatisticsUniversity of Western AustraliaCrawleyAustralia
  3. 3.Department of MathematicsColumbia UniversityNew YorkUSA
  4. 4.School of Mathematics and StatisticsUniversity of MelbourneParkvilleAustralia
  5. 5.Istituto di Matematica Applicata e Tecnologie InformaticheConsiglio Nazionale delle RicerchePaviaItaly

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