Regularity of Jacobians by subdeterminants. (Q1880547)

Some regularity results for the Jacobian determinant of a mapping \(u\in W^{1,n-1} (\Omega,\mathbb{R}^{n})\), having the cofactor matrix of \(Du\) in \(L^{\frac{n}{n-1}} (\Omega)\), in Hardy-Orlicz spaces are given. Among the results are the global integrability of \(J_{u}\log (e+J_{u})\) on \(\Omega\) under some assumptions on the cofactor matrix of \(Du\), and the strong convergence of Jacobians locally on \(\Omega\) in \(L\log L(\Omega)\).