Inserted: 28 oct 2019
Last Updated: 14 sep 2020
Journal: J. Math. Anal. Appl.
In this paper we analyze the asymptotic behavior of the Dirichlet fractional Laplacian on bounded domains that become unbounded in some directions. A dimension reduction phenomenon is observed and described via $\Gamma$-convergence.
Keywords: $\Gamma$-convergence, Variational methods, fractional Laplacian, Asymptotic Analysis