A famous theorem of E. Gagliardo gives the characterization of traces for
Sobolev spaces
W
1
, p
(Ω)
for
1
≤
p<
∞
when
Ω
⊂
R
N
is a Lipschitz domain.
The extension of this result to
W
m, p
(Ω)
for
m
≥
2
and
1
<p<
∞
is now
well-known when
Ω
is a smooth domain. The situation is more complicated for
polygonal and polyhedral domains since the characterization is given only in terms
of local compatibility conditions at the vertices, edges, .... Some recent papers give
the characterization for general Lipschitz domains for m=2 in terms of global
compatibility conditions. Here we give the necessary compatibility conditions for
m
≥
3
and we prove how the local compatibility conditions can be derived.
%0 Journal Article
%1 Geymonat2007Trace
%A Geymonat, Giuseppe
%D 2007
%J Annales mathématiques Blaise Pascal
%K 46e35-sobolev-spaces-and-other-spaces-of-smooth-functions
%N 2
%P 187--197
%R 10.5802/ambp.232
%T Trace Theorems for Sobolev Spaces on Lipschitz Domains. Necessary Conditions
%U http://dx.doi.org/10.5802/ambp.232
%V 14
%X A famous theorem of E. Gagliardo gives the characterization of traces for
Sobolev spaces
W
1
, p
(Ω)
for
1
≤
p<
∞
when
Ω
⊂
R
N
is a Lipschitz domain.
The extension of this result to
W
m, p
(Ω)
for
m
≥
2
and
1
<p<
∞
is now
well-known when
Ω
is a smooth domain. The situation is more complicated for
polygonal and polyhedral domains since the characterization is given only in terms
of local compatibility conditions at the vertices, edges, .... Some recent papers give
the characterization for general Lipschitz domains for m=2 in terms of global
compatibility conditions. Here we give the necessary compatibility conditions for
m
≥
3
and we prove how the local compatibility conditions can be derived.
@article{Geymonat2007Trace,
abstract = {{A famous theorem of E. Gagliardo gives the characterization of traces for
Sobolev spaces
W
1
, p
(Ω)
for
1
≤
p<
∞
when
Ω
⊂
R
N
is a Lipschitz domain.
The extension of this result to
W
m, p
(Ω)
for
m
≥
2
and
1
<p<
∞
is now
well-known when
Ω
is a smooth domain. The situation is more complicated for
polygonal and polyhedral domains since the characterization is given only in terms
of local compatibility conditions at the vertices, edges, .... Some recent papers give
the characterization for general Lipschitz domains for m=2 in terms of global
compatibility conditions. Here we give the necessary compatibility conditions for
m
≥
3
and we prove how the local compatibility conditions can be derived.}},
added-at = {2019-03-01T00:11:50.000+0100},
author = {Geymonat, Giuseppe},
biburl = {https://www.bibsonomy.org/bibtex/28038a592b2c491af1f520e5a2afc4ced/gdmcbain},
citeulike-article-id = {14677458},
citeulike-attachment-1 = {geymonat_07_trace.pdf; /pdf/user/gdmcbain/article/14677458/1151261/geymonat_07_trace.pdf; ac3231f4930dc0791304afa7fab84b48f3690d57},
citeulike-linkout-0 = {http://dx.doi.org/10.5802/ambp.232},
doi = {10.5802/ambp.232},
file = {geymonat_07_trace.pdf},
interhash = {9910128432f3a1247d539b9cdced05aa},
intrahash = {8038a592b2c491af1f520e5a2afc4ced},
issn = {1259-1734},
journal = {Annales math\'{e}matiques Blaise Pascal},
keywords = {46e35-sobolev-spaces-and-other-spaces-of-smooth-functions},
number = 2,
pages = {187--197},
posted-at = {2019-01-07 21:59:17},
priority = {5},
timestamp = {2019-03-01T00:11:50.000+0100},
title = {{Trace Theorems for Sobolev Spaces on Lipschitz Domains. Necessary Conditions}},
url = {http://dx.doi.org/10.5802/ambp.232},
volume = 14,
year = 2007
}