Pohozaev Identities for Anisotropic Integro-differential Operators
نویسندگان
چکیده
We establish Pohozaev identities and integration by parts type formulas for anisotropic integro-differential operators of order 2s, with s ∈ (0, 1). These identities involve local boundary terms, in which the quantity u/d|∂Ω 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 R \ Ω, and d is the distance to ∂Ω.
منابع مشابه
Boundary Regularity, Pohozaev Identities, and Nonexistence Results
In this expository paper we discuss the boundary regularity of solutions to Lu = f(x, u) in Ω, u ≡ 0 in R\Ω, present the Pohozaev identities recently established in [17, 21], and give a sketch of their proofs. The operators L under consideration are integro-differential operator of order 2s, s ∈ (0, 1), the model case being the fractional Laplacian L = (−∆).
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