# Kernel of Trace Operator of Sobolev Spaces on Lipschitz Domain

@article{Hu2020KernelOT, title={Kernel of Trace Operator of Sobolev Spaces on Lipschitz Domain}, author={I-Shing Hu}, journal={arXiv: Analysis of PDEs}, year={2020} }

We are going to show that \[ \overline{C_0^\infty \left(D\right)} = \overline{C_c^\infty \left(D\right)} \] in $W^{1,p}\left(D\right)$, $p\in[1,\infty)$, on Lipschitz domain $D$ by showing both sides are kernel of trace operator \[ T:\,W^{1,p}(D)\rightarrow L^{p}(\partial D). \] In Grisvard's book \cite{key-1}, Corollary this http URL states a much more general result which covers above. But we cannot find a complete proof in literature. Fortunately, we apply some change of variables formulas…

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