Let $u \in [BV(\mathbb R^N)]^N$. We have
$$D^{jump} u(x) = a(x) \otimes b(x)|D^{jump}u|,$$ where $a,b \in \mathbb S^{N-1}$.
What is the projection of $D^{jump}u$ in the direction $a$? And how can we compute $\|D^{jump}u -\text{ projection along a}\|$?
