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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
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