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

We establish an integration by parts formula in bounded domains for the higher order fractional Laplacian $(-Δ)^s$ 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 $s\in(0,1)$. As an immediate consequence of these results, we obtain a unique continuation property for the eigenfunctions $(-Δ)^sϕ=λϕ$ in $Ω$, $ϕ\equiv0$ in $\mathbb R^n\setminusΩ$.

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