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QUASICONFORMAL SOLUTIONS OF POISSON EQUATIONS

Part of: Geometric function theory

Published online by Cambridge University Press:  19 August 2015

PEIJIN LI ,
JIAOLONG CHEN  and
XIANTAO WANG
PEIJIN LI*
Affiliation:
Department of Mathematics, Hunan Normal University, Changsha, Hunan 410081, PR China email wokeyi99@163.com
JIAOLONG CHEN
Affiliation:
Department of Mathematics, Hunan Normal University, Changsha, Hunan 410081, PR China email jiaolongchen@sina.com
XIANTAO WANG
Affiliation:
Department of Mathematics, Shantou University, Shantou, Guangdong 515063, PR China email xtwang@stu.edu.cn
*
✉wokeyi99@163.com
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Abstract

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The main aim of this paper is to establish the Lipschitz continuity of the $(K,K^{\prime })$-quasiconformal solutions of the Poisson equation ${\rm\Delta}w=g$ in the unit disk $\mathbb{D}$.

Keywords

Poisson equationLipschitz continuity(K, K′)-quasiconformal mapping

MSC classification

Primary: 30C65: Quasiconformal mappings in $^n$, other generalizations
Secondary: 30C45: Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.) 30C20: Conformal mappings of special domains

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 92 , Issue 3 , December 2015 , pp. 420 - 428
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

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