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Let $\Omega$, $\Omega'\subset\mathbb{R}^n$ be bounded domains and let$f_m\colon\Omega\to\Omega'$ be a sequence of homeomorphisms with positiveJacobians $J_{f_m} >0$ a.e. and prescribed Dirichlet boundary data. Let all$f_m$ satisfy the Lusin (N) condition and $\sup_m\int_{\Omega}(|Df_m|^{n-1}+A(|\text{cof} Df_m|)+\phi(J_f))<\infty$, where $A$and $\varphi$ are positive convex functions. Let $f$ be a weak limit of $f_m$in $W^{1,n-1}$. Provided certain growth behaviour of $A$ and $\varphi$, we showthat $f$ satisfies the (INV) condition of Conti and De Lellis, the Lusin (N)condition, and polyconvex energies are lower semicontinuous.

Weak limit of homeomorphisms in $W^{1,n-1}$: invertibility and lower semicontinuity of energy