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 $$\Delta u = u''$$
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1If $u$ is a function of time and space then $u''$ can mean derivative wrt time and $\Delta u$ is Laplacian. – Oct 16 '17 at 12:41
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In a context where derivatives make no sense, dashes as in $u''$ might be used to decorate variables. You should provide some context for us to answer your question. – M. Winter Oct 16 '17 at 12:43
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In 1D they're the same, in higher dimensions $u''$ is ambiguous.
Ian
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Can you explain? My PDE notes seem to use them as synonyms regardless of dimension. – mavavilj Oct 16 '17 at 12:52
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@mavavilj Maybe give an example; it would be very strange to use $u''$ as $\Delta u$ in, say, 2D. In part because the Laplacian doesn't really split into two identical operations (it's grad then div). – Ian Oct 16 '17 at 12:54
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Nevermind I made some error in reading, it seems that the case I was reading was actually for $u$ defined on $\mathbb{R}$. So it's used for a 1D case. – mavavilj Oct 16 '17 at 12:57
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