Potential Analysis

, Volume 34, Issue 1, pp 13–22

On Certain Nonlinear Elliptic PDE and Quasiconformal Maps Between Euclidean Surfaces


DOI: 10.1007/s11118-010-9177-x

Cite this article as:
Kalaj, D. & Mateljević, M. Potential Anal (2011) 34: 13. doi:10.1007/s11118-010-9177-x


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 coordinatesHarmonic mapsQuasiconformal mappingsPDELipschitz continuous

Mathematics Subject Classifications (2010)

Primary 30C65; Secondary 53C4330C35

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