A version of Urysohn's Lemma.

Question

For a compact set $K$ of $R^n $ and for an open neighborhood $U$ of $K,$ we know that there exists a smooth, compactly supported function $f\in {\cal C}_c(R^n)$ supported in $U$ which equals $1$ on $K$. Can such function be chosen such that: $ \int_{_{U-K}}(f'(x))^2 dx \to 0, $ as $\mu(U-k)\to 0?$ where $f'$ is the derivative of $f$ and $\mu$ is the ${\cal L}$ebesgue measure.