Strict convergence and minimal liftings in BV

Given a function v is an element of BV(Omega; R-m), we introduce the notion of a minimal lifting of Dv. We prove that every v is an element of BV(Omega; R-m) has a unique minimal lifting, and we show that if v(k) --> v strictly in BV, then the minimal liftings of v(k) converge weakly as measures to the minimal lifting of v. As an application, we deduce a result about weak continuity of the distributional determinant Det D(2)u with respect to strict convergence.