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I want to know the meaning of the statement as below.

$$ \text{There is a sequence} \;\{f_k\} \subset W^{3,2}\; \text{approximating}\;\; f \;\;\text{in}\;\; W^{2,2}. $$

Here $ W^{n,m} $ means a Sobolev Space.

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Presumably this means that each $f_k$ is in $W^{3,2}$ and $f_k \rightarrow f$ in the norm of $W^{2,2}$ (i.e. $\|f_k - f\|_{W^{2,2}} \rightarrow 0$.) –  user15464 May 26 '12 at 20:23
    
@user15464 Thank you very much. –  Misaj May 26 '12 at 20:27
    
@user15464 You could post your comment as an answer. –  Davide Giraudo May 27 '12 at 9:38

1 Answer 1

up vote 1 down vote accepted

Presumably this means that each $f_k$ is in $W^{3,2}$ and $f_k\rightarrow f$ in the norm of $W^{2,2}$ (i.e. $\|f_k-f\|_{W^{2.2}}\rightarrow 0$).

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