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On mappings with integrable dilatation. (English) Zbl 0784.30015

Motivated by recent results on nonlinear elasticity theory the authors show that, under appropriate conditions, a map \(f\in W^{1,2}(G,G')\), where \(G\), \(G'\subset R^ 2\) are bounded domains, admits a Stoilov type factorization and thus, in particular, \(f\) is discrete and open. The crucial conditions are: \(J(x,f)\geq 0\) a.e. and \(K(x)=| Df(x)|^ 2/J(x,f)< \infty\) a.e. The particular case where \(K(x)\leq K\) a.e. in \(G\) is a well-known property of quasiregular maps.

MSC:

30C62 Quasiconformal mappings in the complex plane
35J30 Higher-order elliptic equations
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