Distributional convergence of null Lagrangians under very mild conditions (Q2467061)

Let \(\Omega\) be a bounded connected open subset of \(\mathbb{R}^w\). In the paper there are studied sequences \(U^\varepsilon\) in \(W^{1,m}(\Omega,\mathbb{R}^n)\), \(2\leq m\leq n\). The classical result of convergence in distributional sense of any null Lagrangian states (in particular, that if \(U^\varepsilon\) converges weakly in \(W^{1,m}(\Omega)\) to \(U\), then \(\text{det}(DU^\varepsilon)\) converges to \(\text{det}(DU)\) in \(D'(\Omega)\)) are proved under weaker (special) assumptions.