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Journal of the London Mathematical Society 1999 60(2):561-580; doi:10.1112/S0024610799007851
© 1999 by London Mathematical Society
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© The London Mathematical Society

The Characterization of the Regularity of the Jacobian Determinant in the Framework of Bessel Potential Spaces on Domains

Winfried Sickel and Abdellah Youssfi

Mathematisches Institut, Friedrich-Schiller-Universität Jena Ernst-Abbe-Platz 1–4, 07743 Jena, Germany
Equipe d'Analyse et de Mathématiques Appliquées, Université de Marne-la-Vallée 5 Boulevard Descartes, Cité Descartes Champs-sur-Marne, 77454 Marne-la-Vallée Cedex 2, France

Received 18 November 1997.

Let 2 ≤ m ≤ n. The paper gives necessary and sufficient conditions on the parameters s1, s2, ..., sm, p1, p2, ..., pm such that the Jacobian determinant extends to a bounded operator from Hs1p1 x Hs2p2 x ... x Hsmpm into S'. Here all spaces are defined on Rn or on domains {Omega}subRn. In almost all cases the regularity of the Jacobian determinant is calculated exactly.


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