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

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