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On a new class of elastic deformations not allowing for cavitation. (English) Zbl 0863.49002
The divergence identity $\partial_j\{(g^i\circ u)(\text{adj }Du)^j_i\}= (\text{div }g)\circ\text{det }Du$ is proved under weak assumptions. Also, an integrability result for $$\text{det }Du$$ is proved. As an application, a degree formula is proved in the class $$A_{p,q}(\Omega)$$. As a further application, the existence of an absolutely continuous minimizer of $I(u)=\int_\Omega W(x,u,Du)dx$ is proved if $$W$$ is polyconvex and satisfies the inequality $$W(x,u,F)\geq a(|F|^p+|\text{adj }F|^q)$$ with $$p\geq 2$$ and $$q\geq 3/2$$.

##### MSC:
 49J10 Existence theories for free problems in two or more independent variables 26B10 Implicit function theorems, Jacobians, transformations with several variables 74B20 Nonlinear elasticity
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