Pohozaev identities for anisotropic integro-differential operators
- Ros-Oton, Xavier
- Serra, Joaquim
- Valdinoci, Enrico
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.
- Comm. Partial Differential Equations, 42 (2017), pp. 1290-1321.