Simple bound for $L^p$ norm
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
add a comment |
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
1
thanks im new to Sobolev spaces, maybe add as an answer with a link or something and i can accept it as answer ? :)
– rogerroger
Jan 3 at 12:29
add a comment |
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
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
2,48011431
2,48011431
asked Jan 2 at 21:52
rogerrogerrogerroger
343
343
1
thanks im new to Sobolev spaces, maybe add as an answer with a link or something and i can accept it as answer ? :)
– rogerroger
Jan 3 at 12:29
add a comment |
1
thanks im new to Sobolev spaces, maybe add as an answer with a link or something and i can accept it as answer ? :)
– rogerroger
Jan 3 at 12:29
1
1
thanks im new to Sobolev spaces, maybe add as an answer with a link or something and i can accept it as answer ? :)
– rogerroger
Jan 3 at 12:29
thanks im new to Sobolev spaces, maybe add as an answer with a link or something and i can accept it as answer ? :)
– rogerroger
Jan 3 at 12:29
add a comment |
1 Answer
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It's is just the Sobolev embedding theorem when $p=6$.
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1 Answer
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1 Answer
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It's is just the Sobolev embedding theorem when $p=6$.
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It's is just the Sobolev embedding theorem when $p=6$.
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It's is just the Sobolev embedding theorem when $p=6$.
It's is just the Sobolev embedding theorem when $p=6$.
answered Jan 4 at 3:06
Jacky ChongJacky Chong
17.8k21128
17.8k21128
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thanks im new to Sobolev spaces, maybe add as an answer with a link or something and i can accept it as answer ? :)
– rogerroger
Jan 3 at 12:29