Global higher integrability of Jacobians on bounded domains

We give conditions for a vector-valued function View the MathML source, satisfying View the MathML source on a bounded domain O, which imply that View the MathML source is globally higher integrable on O. We also give conditions for View the MathML source such that View the MathML source belongs to the Hardy space View the MathML source and exhibit some examples which show that our conditions are in some sense optimal. Applications to the weak convergence of Jacobians follow. Div-curl type extensions of these results to forms are also considered.