Asymptotics of solutions of the Dirichlet problem for the Laplace equation in the half-space

This paper is devoted to the study of the asymptotic behavior of the solution of the Dirichlet problem for the Laplace equation in the half-space $E^{N+1}_+ \equiv \{{x,y: x \in E^N, y>0}\}$ for large values of the variable $y$.