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.
Original language | English (US) |
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Pages (from-to) | 539-570 |
Number of pages | 32 |
Journal | Royal Society of Edinburgh - Proceedings A |
Volume | 129 |
Issue number | 3 |
State | Published - Dec 1 1999 |
ASJC Scopus subject areas
- Mathematics(all)