A study of Jacobians in Hardyd–Orlicz spaces

Source abstract

We study the Jacobian determinants J = det(∂ f i /∂ x j ) of mappings f : Ω ⊂ ℝ n → ℝ n in a Sobolev–Orlicz space W 1,Φ (Ω,ℝ n ). Their natural generalizations are the wedge products of differential forms. These products turn out to be in the Hardy–Orlicz spaces ℌ p (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.