Jacobians of BV homeomorphisms and their weak-* limits

Abstract

We prove that in ${\mathbb{R}}^3$ any $BV$ homeomorphism as well as the weak-* limit of $BV$ homeomorphisms cannot change the sign of the Jacobian, i.e., we have $J_f\ge 0$ almost everywhere or $J_f\le 0$ almost everywhere.

arXiv commentSubmitted to Calc. Var