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

David Kalaj

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arXiv · 1009.1133

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

David Kalaj

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Abstract

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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David Kalaj. 2010-09-06. On quasiconformal selfmappings of the unit disk and elliptic PDE in the plane. https://arxiv.org/abs/1009.1133

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