Calculus of Variations and Geometric Measure Theory

V. Ambrosio - L. Freddi - R. Musina

Asymptotic analysis of the Dirichlet fractional Laplacian in domains becoming unbounded

created by freddi on 28 Oct 2019
modified on 14 Sep 2020


Published Paper

Inserted: 28 oct 2019
Last Updated: 14 sep 2020

Journal: J. Math. Anal. Appl.
Volume: 485
Pages: 17
Year: 2020

ArXiv: 1910.11611 PDF


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