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Is there a symbol for the set of twice differentiable functions (2nd derivative not necessarily continuous)? I believe the symbol for twice continuously differentiable functions is $C^2(\mathbb F)$? Thanks

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Given your tag of functional analysis, the following might be of interest for you:

The Sobolev space $W^{k,p}(\Omega)$ is the set of all functions $f \in L^p(\Omega)$ such that for every multi-index $\alpha$ $|α| \leq k$, the weak partial derivative $D^\alpha f$ belongs to $L^p(\Omega)$.

More details in Wikipedia.

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Thanks, George. – gareth Sep 9 '11 at 11:42

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