Simple bound for $L^p$ norm












1














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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    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














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







share|cite|improve this question




















  • 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








1







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







share|cite|improve this question















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






share|cite|improve this question















share|cite|improve this question













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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














  • 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










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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 $p=6$.






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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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        share|cite|improve this answer










        answered Jan 4 at 3:06









        Jacky ChongJacky Chong

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