On the shape of the first fractional eigenfunction

Abstract

We show that the first eigenfunction of the fractional Laplacian ${(-\Delta )}^s$, $s\in (1/2,1)$, is superharmonic in the unitary ball up to dimension $11$. To this aim, we also rely on a computer-assisted step to estimate a rather complicated constant depending on the dimension and the power $s$.

20 pages, 5 figures