Giulio Romani

On the asymptotic behaviour of the restricted Dirichlet Laplacian of real order $s>0$ on stretching tubes

We study spectral and variational properties of the (possibly) fractional Dirichlet Laplacian $\left(-\Delta_{n+k}\right)^s\!$, $s>0$, on bounded subsets of $\mathbb R^n\times\mathbb R^k$ whose extent in one or more directions becomes much larger than in the remaining ones. We first investigate the asymptotic behaviour...