 Special bounded-variation space

A BV space function is special when its derivative has no Cantor part of a bounded-variation derivative: $Du=\nabla udx+[u]{\nu }_u{\mathcal{H}}^{n-1}\lfloor J_u$. The remaining singular part is supported on the jump set of a bounded-variation function. This space accommodates sharp interfaces and is the natural setting for the Mumford–Shah functional.