Asymptotic analysis of the Dirichlet fractional Laplacian in domains becoming unbounded

Abstract

In this paper we analyze the asymptotic behavior of the Dirichlet fractional Laplacian $(-{\Delta }_{{\mathbb{R}}^{n+k}}{)}^s$, with $s\in (0,1)$, on bounded domains in ${\mathbb{R}}^{n+k}$ that become unbounded in the last $k$-directions. A dimension reduction phenomenon is observed and described via $\Gamma$-convergence.

21 pages