WIAS Preprint No. 2080, (2015)

Pohozaev identities for anisotropic integro-differential operators


  • Ros-Oton, Xavier
  • Serra, Joaquim
  • Valdinoci, Enrico
    ORCID: 0000-0001-6222-2272

2010 Mathematics Subject Classification

  • 35R09 47G20 35A01


  • Pohozaev identity, stable Lévy processes, nonlocal operator.




We establish Pohozaev identities and integration by parts type formulas for anisotropic integro-differential operators of order 2s, with s ϵ (0, 1). These identities involve local boundary terms, in which the quantity u/ds ∂Ω plays the role that ∂u/∂v plays in the second order case. Here, u is any solution to Lu = f (x, u) in Ω, with u = 0 in Rn \ Ω , and d is the distance to ∂Ω.

Appeared in

  • Comm. Partial Differential Equations, 42 (2017), pp. 1290-1321.

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