# Projection of BV function

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 $$\|D^{jump}u -\text{ projection along a}\|$$?