Potential Analysis

, Volume 34, Issue 1, pp 13-22

First online:

On Certain Nonlinear Elliptic PDE and Quasiconformal Maps Between Euclidean Surfaces

  • David KalajAffiliated withFaculty of Natural Sciences and Mathematics, University of Montenegro Email author 
  • , Miodrag MateljevićAffiliated withFaculty of Mathematics, University of Belgrade

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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.


Isothermal coordinates Harmonic maps Quasiconformal mappings PDE Lipschitz continuous

Mathematics Subject Classifications (2010)

Primary 30C65; Secondary 53C43 30C35