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arXiv · 1406.1107

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

Xavier Ros-Oton·Joaquim Serra
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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 $s\in(0,1)$. As an immediate consequence of these results, we obtain a unique continuation property for the eigenfunctions $(-\Delta)^s\phi=\lambda\phi$ in $\Omega$, $\phi\equiv0$ in $\mathbb R^n\setminus\Omega$.

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Xavier Ros-Oton, Joaquim Serra. 2014-06-04. Local integration by parts and Pohozaev identities for higher order fractional Laplacians. https://arxiv.org/abs/1406.1107

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