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A study of Jacobians in Hardyd–Orlicz spaces

Published online by Cambridge University Press:  14 November 2011

Tadeusz Iwaniec
Affiliation:
Department of Mathematics, Syracuse University, Syracuse, NY 13244, USA
Anna Verde
Affiliation:
Dipartimento di Matematica e Applicazioni, R. Caccioppoli, Via Cintia, 80126 Napoli, Italy

Abstract

We study the Jacobian determinants J = det(∂fi/∂xj) of mappings f: Ω ⊂ ℝn → ℝn in a Sobolev–Orlicz space W1,Φ (Ω,ℝn). Their natural generalizations are the wedge products of differential forms. These products turn out to be in the Hardy–Orlicz spaces ℌp (Ω). Other nonlinear quantities involving the Jacobian, such as J log |J|, are also studied. In general, the Jacobians may change sign and in this sense our results generalize the existing ones concerning positive Jacobians.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 1999

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