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For example, I want to know that the statements as below.

(1) there is a sequence $\{ f_k \} \subset W^{3,2}$ approximating $f$ in $W^{2,2}$.

(2) we can approximate $f$ in $K \subset R^n$ by a sequence of functions $\{ f_k \}$ in $W^{2,2}(K)$.

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It means, for the first question, that $\lVert f_k-f\rVert_{W^{2,2}}\to 0$ when $k\to +\infty$. For the second one, that $\lVert f_k-f\rVert_{W^{2,2}(K)}\to 0$ when $k\to +\infty$.

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