Local integration by parts and Pohozaev identities for higher order fractional Laplacians
2014; American Institute of Mathematical Sciences; Volume: 35; Issue: 5 Linguagem: Inglês
10.3934/dcds.2015.35.2131
ISSN1553-5231
AutoresXavier Ros‐Oton, Joaquim Serra,
Tópico(s)Numerical methods in inverse problems
ResumoWe 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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