, Volume 34, Issue 1, pp 13-22
Date: 05 May 2010

On Certain Nonlinear Elliptic PDE and Quasiconformal Maps Between Euclidean Surfaces

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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.