Dependance of constants on size of the domain [on hold]












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Let $B$ be the unit ball.
Suppose I have a constant $C>0$ so that $forall u in C^{1}_{0}(B)$:



$int_{B} |D^{2}u|^{2} le C int_{B}|Delta u|^{2} $



Can I get the same constant for a larger Ball $B_{2}$ and thus for any radius?



Any help would be appreciated!










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put on hold as off-topic by Nosrati, Adrian Keister, José Carlos Santos, KReiser, Leucippus Jan 8 at 3:28


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Nosrati, Adrian Keister, José Carlos Santos, KReiser, Leucippus

If this question can be reworded to fit the rules in the help center, please edit the question.


















    0












    $begingroup$


    Let $B$ be the unit ball.
    Suppose I have a constant $C>0$ so that $forall u in C^{1}_{0}(B)$:



    $int_{B} |D^{2}u|^{2} le C int_{B}|Delta u|^{2} $



    Can I get the same constant for a larger Ball $B_{2}$ and thus for any radius?



    Any help would be appreciated!










    share|cite|improve this question









    $endgroup$



    put on hold as off-topic by Nosrati, Adrian Keister, José Carlos Santos, KReiser, Leucippus Jan 8 at 3:28


    This question appears to be off-topic. The users who voted to close gave this specific reason:


    • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Nosrati, Adrian Keister, José Carlos Santos, KReiser, Leucippus

    If this question can be reworded to fit the rules in the help center, please edit the question.
















      0












      0








      0





      $begingroup$


      Let $B$ be the unit ball.
      Suppose I have a constant $C>0$ so that $forall u in C^{1}_{0}(B)$:



      $int_{B} |D^{2}u|^{2} le C int_{B}|Delta u|^{2} $



      Can I get the same constant for a larger Ball $B_{2}$ and thus for any radius?



      Any help would be appreciated!










      share|cite|improve this question









      $endgroup$




      Let $B$ be the unit ball.
      Suppose I have a constant $C>0$ so that $forall u in C^{1}_{0}(B)$:



      $int_{B} |D^{2}u|^{2} le C int_{B}|Delta u|^{2} $



      Can I get the same constant for a larger Ball $B_{2}$ and thus for any radius?



      Any help would be appreciated!







      analysis






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      share|cite|improve this question











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      asked Jan 7 at 11:55









      Falc14Falc14

      12




      12




      put on hold as off-topic by Nosrati, Adrian Keister, José Carlos Santos, KReiser, Leucippus Jan 8 at 3:28


      This question appears to be off-topic. The users who voted to close gave this specific reason:


      • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Nosrati, Adrian Keister, José Carlos Santos, KReiser, Leucippus

      If this question can be reworded to fit the rules in the help center, please edit the question.




      put on hold as off-topic by Nosrati, Adrian Keister, José Carlos Santos, KReiser, Leucippus Jan 8 at 3:28


      This question appears to be off-topic. The users who voted to close gave this specific reason:


      • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Nosrati, Adrian Keister, José Carlos Santos, KReiser, Leucippus

      If this question can be reworded to fit the rules in the help center, please edit the question.






















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