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Det$$=\det$$. A remark on the distributional determinant. (English. Abridged French version) Zbl 0717.46033
The aim of the paper is to prove a conjecture of J. M. Ball concerning the distributional determinant. The main result consists in a theorem showing that if $$[\Omega \subset {\mathbb{R}}^ n$$ is open; $$1\leq p<n$$; $$v\in W^{1,p}(\Omega)$$; $$\sigma \in L^ q(\Omega;{\mathbb{R}}^ 2)$$ with $$(1/p)- (1/n)+(1/q)\leq 1$$; the distributional divergence of $$\sigma$$ satisfies $$text{div}\sigma\in L^ 1(\Omega)$$; the distribution $$d=text{div}(v\sigma)$$ satisfies $$d\in L^ 1(\Omega);]$$ then $[d(x)=Dv(x)\sigma(x)+v(x) text{div}\sigma(x)\text{, for a.e. }x\in \Omega].$
Reviewer: L.Goras

##### MSC:
 46F10 Operations with distributions and generalized functions