In this paper, we propose a new numerical method for solving
elliptic equations in unbounded regions of ${\mathbb{R}}^n$. The
method is based on the mapping of a part of the domain into a
bounded region. An appropriate family of weighted spaces is used
for describing the growth or the decay of functions at large distances. After
exposing the main ideas of the method, we analyse
carefully its convergence. Some 3D computational results are displayed
to demonstrate its efficiency and its high performance.