Local integration by parts and Pohozaev indentities for higuer order fractional Laplacians

Abstract

We establish an integration by parts formula in bounded domains for the higher order fractional Laplacian (-Delta)(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 is an element of (0,1).; As an immediate consequence of these results, we obtain a unique continuation property for the eigenfunctions (-Delta)(s)phi = lambda phi in Omega, phi equivalent to 0 in R-n\Omega.