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THE CHARACTERIZATION OF THE REGULARITY OF THE JACOBIAN DETERMINANT IN THE FRAMEWORK OF BESSEL POTENTIAL SPACES ON DOMAINS

Published online by Cambridge University Press:  01 October 1999

WINFRIED SICKEL  and
ABDELLAH YOUSSFI
WINFRIED SICKEL
Affiliation:
Mathematisches Institut, Friedrich-Schiller-Universität Jena, Ernst-Abbe-Platz 1–4, 07743 Jena, Germany
ABDELLAH YOUSSFI
Affiliation:
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
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Abstract

Let 2 [les ] m [les ] 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 [Hscr ]s1p1 × [Hscr ]s2p2 × … × [Hscr ]smpm into [Sscr ]′. Here all spaces are defined on ℝn or on domains Ω⊂ℝn. In almost all cases the regularity of the Jacobian determinant is calculated exactly.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 60 , Issue 2 , October 1999 , pp. 561 - 580
Copyright
The London Mathematical Society 1999

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