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We prove the following theorem: if $w$ is a quasiconformal mapping of theunit 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 ellipticdifferential operator is {only} considered {the} Laplace operator.

On quasiconformal selfmappings of the unit disk and elliptic PDE in the plane