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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
David Kalaj*
Affiliation:
Faculty of Natural Sciences and Mathematics, University of Montenegro, Dzordza Vasingtona b.b., 81000 Podgorica, Montenegro (davidk@ac.me)
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Abstract

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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
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 143 , Issue 4 , August 2013 , pp. 831 - 849
Copyright
Copyright © Royal Society of Edinburgh 2013