Pohozaev identities for anisotropic integro-differential operators

2015/02/05 by Xavier Ros-Oton, Joaquim Serra, Ros-Oton, Xavier +3 · 2 citations
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.1502.01431

arxiv created 2016/01/08 · arxiv updated 2016/01/12

Abstract

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^s|_∂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 \mathbb Rⁿ∖Ω, and d is the distance to ∂Ω.

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