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 Sobolev spaces on Lipschitz domains by taking advantage of the intrinsic norm on \$H^s (\partialØmega)\$. It is proved that the trace operator is a linear bounded operator from \$H^s (Ømega)\$ to \$H^s-12 (\partialØmega)\$ for \$12 < s < 32\$.
%0 Journal Article
%1 Ding1996Proof
%A Ding, Zhonghai
%D 1996
%J Proceedings of the American Mathematical Society
%K 46e35-sobolev-spaces-and-other-spaces-of-smooth-functions
%N 2
%P 591--600
%R 10.1090/s0002-9939-96-03132-2
%T A Proof of the Trace Theorem of Sobolev Spaces on Lipschitz Domains
%U http://dx.doi.org/10.1090/s0002-9939-96-03132-2
%V 124
%X 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 Sobolev spaces on Lipschitz domains by taking advantage of the intrinsic norm on \$H^s (\partialØmega)\$. It is proved that the trace operator is a linear bounded operator from \$H^s (Ømega)\$ to \$H^s-12 (\partialØmega)\$ for \$12 < s < 32\$.
@article{Ding1996Proof,
abstract = {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 Sobolev spaces on Lipschitz domains by taking advantage of the intrinsic norm on \$H^s (\partial\Omega)\$. It is proved that the trace operator is a linear bounded operator from \$H^s (\Omega)\$ to \$H^{s-\frac{1}{2}} (\partial\Omega)\$ for \$\frac{1}{2} < s < \frac{3}{2}\$.},
added-at = {2019-03-01T00:11:50.000+0100},
author = {Ding, Zhonghai},
biburl = {https://www.bibsonomy.org/bibtex/24d00f2217c4e8c44094fd898746a3ae1/gdmcbain},
citeulike-article-id = {14677457},
citeulike-attachment-1 = {ding_96_proof_1151260.pdf; /pdf/user/gdmcbain/article/14677457/1151260/ding_96_proof_1151260.pdf; 2ca34fda171f106ce936df534ad719c658ed90f0},
citeulike-linkout-0 = {http://dx.doi.org/10.1090/s0002-9939-96-03132-2},
doi = {10.1090/s0002-9939-96-03132-2},
file = {ding_96_proof_1151260.pdf},
interhash = {4554c68462eab4a838112b06111be7e4},
intrahash = {4d00f2217c4e8c44094fd898746a3ae1},
issn = {0002-9939},
journal = {Proceedings of the American Mathematical Society},
keywords = {46e35-sobolev-spaces-and-other-spaces-of-smooth-functions},
number = 2,
pages = {591--600},
posted-at = {2019-01-07 21:52:04},
priority = {5},
timestamp = {2019-03-01T00:11:50.000+0100},
title = {A Proof of the Trace Theorem of {S}obolev Spaces on {L}ipschitz Domains},
url = {http://dx.doi.org/10.1090/s0002-9939-96-03132-2},
volume = 124,
year = 1996
}