On the Asymptotic Analysis of Problems Involving Fractional Laplacian in Cylindrical Domains Tending to Infinity

Indranil Chowdhury, Prosenjit Roy

Published 2015-09-22Version 1

The article is an attempt to investigate the issues of asymptotic analysis for problems involving fractional Laplacian where the domains tend to become unbounded in one-direction. Motivated from the pioneering work on second order elliptic problems by Chipot and Rougirel, where the force functions are considered on the cross section of domains, we prove the non-local counterpart of their result. Furthermore, recently Yeressian established the asymptotic behaviors for solutions of non local Dirichlet problems when the force functions are supported at the end of the domain. However, their result holds only for the case of fractional Laplacian of order 1/2 . In this article, we extend this result to each order between 0 to 1.