On certain nonlinear elliptic PDE and quasiconfomal mapps between Euclidean surfaces

David Kalaj; Miodrag Mateljevic

On certain nonlinear elliptic PDE and quasiconfomal mapps between Euclidean surfaces

Complex Variables 2012-02-21 v2 Analysis of PDEs

Authors: David Kalaj , Miodrag Mateljevic

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 that these mappings are Lipschitz. Conformal parametrization of such surfaces and the method developed in our paper \cite{km} have important role in this paper.dan curves and is extended to the case of $C^{2,\alpha}$ surfaces with smooth and compact boundary.

Keywords

differential geometry of surfaces and curves in euclidean space surface theory surfaces with constant mean curvature

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@article{arxiv.0804.2785,
  title  = {On certain nonlinear elliptic PDE and quasiconfomal mapps between Euclidean surfaces},
  author = {David Kalaj and Miodrag Mateljevic},
  journal= {arXiv preprint arXiv:0804.2785},
  year   = {2012}
}

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9 pages

On certain nonlinear elliptic PDE and quasiconfomal mapps between Euclidean surfaces

Abstract

Keywords

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