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

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

2010-09-06

arxiv.org/abs/1009.1133v2

Mathematics

Analysis of PDEs

19 pages

Scientific paper

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.

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