Compactness of the trace operator of the Sobolev space

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Show that the trace operator $$T:W^{1,p}(\Omega)\rightarrow L^p(\partial\Omega)$$ is compact.

I have searched the questions online and looked it up in several references listed below:

1.Lawrence C.Evans, Partial Differential Equations, Second Edition

2.Giovanni Leoni, A First Course in Sobolev Space

3.https://www.math.kit.edu/iana2/lehre/sobolevspaces2021s/media/lec15.pdf

But I don't find a direct proof of the case I put on here. I am confused about what tools I should use, Arzela-Asocoli Lemma?