Is $u''$ always synonymous to $\Delta u$?

Question

Is $u''$ always synonymous to $\Delta u$?

Or if not, then what does $u''$ refer to?

This is in contexts of giving PDE problems e.g. as:

$$\Delta u = 0$$

Sometimes I see

$$u'' = 0$$

Can I assume in this case that $$\Delta u = u''$$

Answer 1

In 1D they're the same, in higher dimensions $u''$ is ambiguous.