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

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