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Sobolev versus homogeneous Sobolev extension II
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Abstract
We study the relationship between Sobolev extension domains and homogeneous Sobolev extension domains. Precisely, for a certain range of exponents
p
and
q
, we construct a
$$(W^{1, p}, W^{1, q})$$
(
W
1
,
p
,
W
1
,
q
)
-extension domain which is not an
$$(L^{1, p}, L^{1, q})$$
(
L
1
,
p
,
L
1
,
q
)
-extension domain.
Springer Science and Business Media LLC
Title: Sobolev versus homogeneous Sobolev extension II
Description:
Abstract
We study the relationship between Sobolev extension domains and homogeneous Sobolev extension domains.
Precisely, for a certain range of exponents
p
and
q
, we construct a
$$(W^{1, p}, W^{1, q})$$
(
W
1
,
p
,
W
1
,
q
)
-extension domain which is not an
$$(L^{1, p}, L^{1, q})$$
(
L
1
,
p
,
L
1
,
q
)
-extension domain.
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