On the First Eigenfunction of the Symmetric Stable Process in a Bounded Lipschitz Domain

We give a proof that the first eigenfunction of the $α$-symmetric stable process on a bounded Lipschitz domain in $\R^d$, $d\geq 1$, is superharmonic for $α=2/m$, where $m>2$ is an integer. This result was first proved for the ball by M. Kaßmann and L. Silvestre (personal communication) with different methods. For $α=1$, the result was proved in \cite[Theorem 4.7]{BanKul}.

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