Abstract.
Let \(f:\Omega \rightarrow{\Bbb R}^n\) be a mapping in the Sobolev space \(W^{1,n-1}_{loc}(\Omega,{\Bbb R}^n), n\geq 2\). We assume that the cofactors of the differential matrix Df(x) belong to \(L^\frac{n}{n-1}(\Omega)\). Then, among other things, we prove that the Jacobian determinant detDf lies in the Hardy space \({\cal H}^1(\Omega)\).
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Received: 20 November 2000 / Revised version: 17 December 2001 / Published online: 5 September 2002
Iwaniec was supported by NSF grant DMS-0070807. This research was done while Onninen was visiting Mathematics Department at Syracuse University. He wishes to thank SU for the support and hospitality.
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Iwaniec, T., Onninen, J. \({\cal H}^1\)-estimates of Jacobians by subdeterminants. Math Ann 324, 341–358 (2002). https://doi.org/10.1007/s00208-002-0341-5
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DOI: https://doi.org/10.1007/s00208-002-0341-5