$V$ is Compactly Embbeded in it self?

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Can we say that $V$ is compactly embbeded in it self

$$V=\left\{u\in H^{1}\left(\Omega\right):\gamma_{0}\left(u\right)=0 \text{ on } \Gamma_{0}\right\}$$

I would like to use aubin-lions theorem.