• Corpus ID: 216867983

# 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}
}
• I-Shing Hu
• Published 29 April 2020
• Mathematics
• arXiv: Analysis of PDEs
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…

## References

SHOWING 1-6 OF 6 REFERENCES

A complete proof of the trace theorem of Sobolev spaces on Lipschitz domains has not appeared in the literature yet. The purpose of this paper is to give a complete proof of the trace theorem of
Foreword Preface 1. Sobolev spaces 2. Regular second-order elliptic boundary value problems 3. Second-order elliptic boundary value problems in convex domains 4. Second-order boundary value problems
• Mathematics
• 2012
1.Introduction to the problem.- 2.Sobolev spaces.- 3.Exitence, Uniqueness of basic problems.- 4.Regularity of solution.- 5.Applications of Rellich's inequalities and generalization to boundary value