Asymptotic behavior of elliptic nonlocal equations set in cylinders

In this paper the asymptotic behavior of elliptic nonlocal equations in cylindrical domains is studied. These equations are associated with symmetric pure jump Lévy stochastic processes and are generalisation of equations involving the fractional Laplacian operator. First we consider the existence and uniqueness of weak solutions in appropriate Hilbert spaces associated with the Lévy measure and then study the asymptotic behavior in cylinders.