  We prove the following theorem: if $w$ is a quasiconformal mapping of the
unit disk onto itself satisfying elliptic partial differential inequality
$|L[w]|\le \mathcal{B}|\nabla w|^2+\Gamma$, then $w$ is Lipschitz continuous.
This {result} extends some recent results, where instead of an elliptic
differential operator is {only} considered {the} Laplace operator.
