Simple bound for $L^p$ norm
$begingroup$
Is there a bound for any $1<p<infty$ or specifically $p=6$ such that
$$||u||_{L^{p}(U)}leq C ||u||_{H^{1}(U)} $$
Where $U$ is an open bounded set of class $C^2$ in $mathbb{R^3}$
and $H^{1}$ is the usual Sobolev norm.
functional-analysis banach-spaces sobolev-spaces lp-spaces
edited Jan 4 at 3:33
the_fox
2,90021537
asked Jan 2 at 21:52
rogerrogerrogerroger
343
$endgroup$
add a comment |
$begingroup$
Is there a bound for any $1<p<infty$ or specifically $p=6$ such that
$$||u||_{L^{p}(U)}leq C ||u||_{H^{1}(U)} $$
Where $U$ is an open bounded set of class $C^2$ in $mathbb{R^3}$
and $H^{1}$ is the usual Sobolev norm.
functional-analysis banach-spaces sobolev-spaces lp-spaces
edited Jan 4 at 3:33
the_fox
2,90021537
asked Jan 2 at 21:52
rogerrogerrogerroger
343
$endgroup$
1
$begingroup$
thanks im new to Sobolev spaces, maybe add as an answer with a link or something and i can accept it as answer ? :)
$endgroup$
– rogerroger
Jan 3 at 12:29
add a comment |
$begingroup$
Is there a bound for any $1<p<infty$ or specifically $p=6$ such that
$$||u||_{L^{p}(U)}leq C ||u||_{H^{1}(U)} $$
Where $U$ is an open bounded set of class $C^2$ in $mathbb{R^3}$
and $H^{1}$ is the usual Sobolev norm.
functional-analysis banach-spaces sobolev-spaces lp-spaces
edited Jan 4 at 3:33
the_fox
2,90021537
asked Jan 2 at 21:52
rogerrogerrogerroger
343
$endgroup$
Is there a bound for any $1<p<infty$ or specifically $p=6$ such that
$$||u||_{L^{p}(U)}leq C ||u||_{H^{1}(U)} $$
Where $U$ is an open bounded set of class $C^2$ in $mathbb{R^3}$
and $H^{1}$ is the usual Sobolev norm.
functional-analysis banach-spaces sobolev-spaces lp-spaces
functional-analysis banach-spaces sobolev-spaces lp-spaces
edited Jan 4 at 3:33
the_fox
2,90021537
asked Jan 2 at 21:52
rogerrogerrogerroger
343
edited Jan 4 at 3:33
the_fox
2,90021537
asked Jan 2 at 21:52
rogerrogerrogerroger
343
edited Jan 4 at 3:33
the_fox
2,90021537
edited Jan 4 at 3:33
the_fox
2,90021537
edited Jan 4 at 3:33
the_fox
2,90021537
2,90021537
asked Jan 2 at 21:52
rogerrogerrogerroger
343
asked Jan 2 at 21:52
rogerrogerrogerroger
343
asked Jan 2 at 21:52
rogerrogerrogerroger
343
343
1
$begingroup$
thanks im new to Sobolev spaces, maybe add as an answer with a link or something and i can accept it as answer ? :)
$endgroup$
– rogerroger
Jan 3 at 12:29
add a comment |
1
$begingroup$
thanks im new to Sobolev spaces, maybe add as an answer with a link or something and i can accept it as answer ? :)
$endgroup$
– rogerroger
Jan 3 at 12:29
1
1
$begingroup$
thanks im new to Sobolev spaces, maybe add as an answer with a link or something and i can accept it as answer ? :)
$endgroup$
– rogerroger
Jan 3 at 12:29
$begingroup$
thanks im new to Sobolev spaces, maybe add as an answer with a link or something and i can accept it as answer ? :)
$endgroup$
– rogerroger
Jan 3 at 12:29
add a comment |
1 Answer
1
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$begingroup$
It's is just the Sobolev embedding theorem when $p=6$.
answered Jan 4 at 3:06
Jacky ChongJacky Chong
19k21129
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add a comment |
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$begingroup$
It's is just the Sobolev embedding theorem when $p=6$.
answered Jan 4 at 3:06
Jacky ChongJacky Chong
19k21129
$endgroup$
add a comment |
$begingroup$
It's is just the Sobolev embedding theorem when $p=6$.
answered Jan 4 at 3:06
Jacky ChongJacky Chong
19k21129
$endgroup$
add a comment |
$begingroup$
It's is just the Sobolev embedding theorem when $p=6$.
answered Jan 4 at 3:06
Jacky ChongJacky Chong
19k21129
$endgroup$
It's is just the Sobolev embedding theorem when $p=6$.
answered Jan 4 at 3:06
Jacky ChongJacky Chong
19k21129
answered Jan 4 at 3:06
Jacky ChongJacky Chong
19k21129
answered Jan 4 at 3:06
Jacky ChongJacky Chong
19k21129
answered Jan 4 at 3:06
Jacky ChongJacky Chong
19k21129
19k21129
add a comment |
add a comment |
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$begingroup$
thanks im new to Sobolev spaces, maybe add as an answer with a link or something and i can accept it as answer ? :)
$endgroup$
– rogerroger
Jan 3 at 12:29