Local integration by parts and Pohozaev identities for higher order fractional Laplacians

Abstract. We establish an integration by parts formula in bounded domains for the higher order fractional Laplacian (−∆)s with s> 1. We also obtain the Pohozaev identity for this operator. Both identities involve local boundary terms, and they extend the identities obtained by the authors in the case s ∈ (0, 1). As an immediate consequence of these results, we obtain a unique continuation property for the eigenfunctions (−∆)sφ = λφ in Ω, φ ≡ 0 in Rn \ Ω