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On quasi-conformal self-mappings of the unit disc and elliptic PDEs in the plane

Published online by Cambridge University Press:  17 July 2013

David Kalaj*
Affiliation:
Faculty of Natural Sciences and Mathematics, University of Montenegro, Dzordza Vasingtona b.b., 81000 Podgorica, Montenegro ([email protected])

Abstract

We prove the following theorem: if w is a quasi-conformal mapping of the unit disc onto itself satisfying elliptic partial differential inequality , then w is Lipschitz continuous. This result extends some recent results where, instead of an elliptic differential operator, only the Laplace operator is considered.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2013 

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