Pohozaev identities for anisotropic integro-differential operators

摘要

We establish Pohozaev identities and integration by parts type formulas foranisotropic integro-differential operators of order $2s$, with $s\in(0,1)$. These identities involve local boundary terms, in which the quantity$u/d^s|_{\partial\Omega}$ plays the role that $\partial u/\partial\nu$ plays inthe second order case. Here, $u$ is any solution to $Lu=f(x,u)$ in $\Omega$,with $u=0$ in $\mathbb R^n\setminus\Omega$, and $d$ is the distance to$\partial\Omega$.