Potential Analysis

, Volume 34, Issue 1, pp 13–22 | Cite as

On Certain Nonlinear Elliptic PDE and Quasiconformal Maps Between Euclidean Surfaces

Article

Abstract

We mainly investigate some properties of quasiconformal mappings between smooth 2-dimensional surfaces with boundary in the Euclidean space, satisfying certain partial differential equations (inequalities) concerning Laplacian, and in particular satisfying Laplace equation and show that these mappings are Lipschitz. Conformal parametrization of such surfaces and the method developed in our paper (Kalaj and Mateljević, J Anal Math 100:117–132, 2006) have important role in this paper.

Keywords

Isothermal coordinates Harmonic maps Quasiconformal mappings PDE Lipschitz continuous 

Mathematics Subject Classifications (2010)

Primary 30C65; Secondary 53C43 30C35 

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Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Faculty of Natural Sciences and MathematicsUniversity of MontenegroPodgoricaMontenegro
  2. 2.Faculty of MathematicsUniversity of BelgradeBelgradeSerbia

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