We find and prove new Pohozaev identities and integration by parts type formulas for anisotropic integrodifferential operators of order 2s, with s∈(0,1). These identities involve local boundary terms, in which the quantity plays the role that ∂u∕∂ν 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.

Pohozaev identities for anisotropic integrodifferential operators / X. Ros-Oton, J. Serra, E. Valdinoci. - In: COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0360-5302. - 42:8(2017), pp. 1290-1321. [10.1080/03605302.2017.1349148]

Pohozaev identities for anisotropic integrodifferential operators

E. Valdinoci
Ultimo
2017

Abstract

We find and prove new Pohozaev identities and integration by parts type formulas for anisotropic integrodifferential operators of order 2s, with s∈(0,1). These identities involve local boundary terms, in which the quantity plays the role that ∂u∕∂ν 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.
nonlocal operator; Pohozaev identity; stable Lévy processes; analysis; applied mathematics
Settore MAT/05 - Analisi Matematica
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/549553
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