A new approach to topological singularities via a weak notion of Jacobian for functions of bounded variation

Lucia De Luca, Riccardo Scala, Nicolas Van Goethem

We introduce a weak notion of $2\times 2$-minors of gradients of a suitable subclass of $BV$ functions. In the case of maps in $BV({\mathbb{R}}^2;{\mathbb{R}}^2)$ such a notion extends…