TY - JOUR
T1 - A study of Jacobians in Hardy-Orlicz spaces
AU - Iwaniec, Tadeusz
AU - Verde, Anna
PY - 1999
Y1 - 1999
N2 - 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.
AB - 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.
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U2 - 10.1017/s0308210500021508
DO - 10.1017/s0308210500021508
M3 - Article
AN - SCOPUS:22644450595
SN - 0308-2105
VL - 129
SP - 539
EP - 570
JO - Royal Society of Edinburgh - Proceedings A
JF - Royal Society of Edinburgh - Proceedings A
IS - 3
ER -