Simple bound for $L^p$ norm












1












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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.










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  • 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












$begingroup$


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.










share|cite|improve this question











$endgroup$








  • 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














1












1








1





$begingroup$


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.










share|cite|improve this question











$endgroup$




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






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edited Jan 4 at 3:33









the_fox

2,58711533




2,58711533










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














  • 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










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It's is just the Sobolev embedding theorem when $p=6$.






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    $begingroup$

    It's is just the Sobolev embedding theorem when $p=6$.






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      0












      $begingroup$

      It's is just the Sobolev embedding theorem when $p=6$.






      share|cite|improve this answer









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        $begingroup$

        It's is just the Sobolev embedding theorem when $p=6$.






        share|cite|improve this answer









        $endgroup$



        It's is just the Sobolev embedding theorem when $p=6$.







        share|cite|improve this answer












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        answered Jan 4 at 3:06









        Jacky ChongJacky Chong

        17.9k21128




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