## 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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### References:

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