  Let $\overline{\mathbb{D}}$ be the closure of the unit disk $\mathbb{D}$ in
the complex plane $\mathbb{C}$ and $g$ be a continuous function in
$\overline{\mathbb{D}}$. In this paper, we discuss some characterizations of
elliptic mappings $f$ satisfying the Poisson's equation $\Delta f=g$ in
$\mathbb{D}$, and then establish some sharp distortion theorems on elliptic
mappings with the finite perimeter and the finite radial length, respectively.
The obtained results are the extension of the corresponding classical results.
