Strict convergence and minimal liftings in BV

Source abstract

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