Symmetry and maximum value [closed]The mean value property and local maximumto show $g$ attains maxima and...

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Symmetry and maximum value [closed]


The mean value property and local maximumto show $g$ attains maxima and minimaLocal maximum and negative definitenessAttempt at Proving A Lemma (critical point, 2nd derivative, global maximum).The symmetry of mixed partials, for derivatives of order > 2Limit and maximum: IVTSymmetry in partial derivatives.If $A$ has a maximum, prove that it only has one.Maximum of function$(a, b) = left{x in mathbb{R}: a < x < bright}$ has neither minimum nor maximum.













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$begingroup$


Assuming $U(x)>0$ is radial symmetric,and $U(x)$ is decrease respect to $|x|$, and $Uin H^2(mathbb R^n)$.



For any $||u||_{L^2}=1$, if $u$ make
$$
int Uu
$$

bs maximum, how to show $u$ is radial symmetric ?










share|cite|improve this question









$endgroup$



closed as off-topic by Alex Provost, Abcd, RRL, Eevee Trainer, Shailesh Mar 13 at 0:31


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." – RRL, Eevee Trainer, Shailesh

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





















    -2












    $begingroup$


    Assuming $U(x)>0$ is radial symmetric,and $U(x)$ is decrease respect to $|x|$, and $Uin H^2(mathbb R^n)$.



    For any $||u||_{L^2}=1$, if $u$ make
    $$
    int Uu
    $$

    bs maximum, how to show $u$ is radial symmetric ?










    share|cite|improve this question









    $endgroup$



    closed as off-topic by Alex Provost, Abcd, RRL, Eevee Trainer, Shailesh Mar 13 at 0:31


    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." – RRL, Eevee Trainer, Shailesh

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



















      -2












      -2








      -2





      $begingroup$


      Assuming $U(x)>0$ is radial symmetric,and $U(x)$ is decrease respect to $|x|$, and $Uin H^2(mathbb R^n)$.



      For any $||u||_{L^2}=1$, if $u$ make
      $$
      int Uu
      $$

      bs maximum, how to show $u$ is radial symmetric ?










      share|cite|improve this question









      $endgroup$




      Assuming $U(x)>0$ is radial symmetric,and $U(x)$ is decrease respect to $|x|$, and $Uin H^2(mathbb R^n)$.



      For any $||u||_{L^2}=1$, if $u$ make
      $$
      int Uu
      $$

      bs maximum, how to show $u$ is radial symmetric ?







      analysis






      share|cite|improve this question













      share|cite|improve this question











      share|cite|improve this question




      share|cite|improve this question










      asked Mar 12 at 13:56









      lanse7ptylanse7pty

      1,8121823




      1,8121823




      closed as off-topic by Alex Provost, Abcd, RRL, Eevee Trainer, Shailesh Mar 13 at 0:31


      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." – RRL, Eevee Trainer, Shailesh

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







      closed as off-topic by Alex Provost, Abcd, RRL, Eevee Trainer, Shailesh Mar 13 at 0:31


      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." – RRL, Eevee Trainer, Shailesh

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






















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