On certain nonlinear elliptic PDE and quasiconfomal mapps between Euclidean surfaces

Details On certain nonlinear elliptic PDE and quasiconfomal mapps between Euclidean surfaces On certain nonlinear elliptic PDE and quasiconfomal mapps between Euclidean surfaces

2008-04-17

arxiv.org/abs/0804.2785v2

Potential analysis, Volume 34, Number 1, 13-22, (2011)

Mathematics

Complex Variables

9 pages

Scientific paper

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.

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