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?