I am trying to find $\frac{\partial ^2}{\partial r^2} \frac{1}{|\partial B(x,r)|} \int_{\partial B(x,r)} u(y,t)\mathrm{d}y $ . Where $B$ is a ball of radius $r$ with center at $x$ .

Differentiating once was ok , but i couldn't not again differentiate .

Thank you for your help .

  • $\begingroup$ What's "average" doing in there? $\endgroup$
    – joriki
    Jul 10, 2012 at 10:40
  • $\begingroup$ @joriki : I don't know how to make it $\int$ with the cut , ie average of surface integral . $\endgroup$
    – Theorem
    Jul 10, 2012 at 10:42
  • $\begingroup$ AFAIK the \strokedint or \fint commands are not implemented in MathJax, so I just replaced it by the definition. $\endgroup$ Jul 10, 2012 at 11:02
  • $\begingroup$ @WillieWong : Thank you . $\endgroup$
    – Theorem
    Jul 10, 2012 at 11:06

1 Answer 1


You can find it in the first section of chapter 5 of the classical book by Fritz John Partial Differential equations (and in many other books on PDE's).


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