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

Anna Doležalová, Stanislav Hencl, Anastasia Molchanova

Let $\Omega$, ${\Omega }^{\prime }\subset {\mathbb{R}}^n$ be bounded domains and let $f_m:\Omega \to {\Omega }^{\prime }$ be a sequence of homeomorphisms with positive Jacobians $J_{f_m}>0$ a.e. and prescribed Dirichlet bou…