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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 .

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What's "average" doing in there? –  joriki Jul 10 '12 at 10:40
    
@joriki : I don't know how to make it $\int$ with the cut , ie average of surface integral . –  Theorem Jul 10 '12 at 10:42
    
AFAIK the \strokedint or \fint commands are not implemented in MathJax, so I just replaced it by the definition. –  Willie Wong Jul 10 '12 at 11:02
    
@WillieWong : Thank you . –  Theorem Jul 10 '12 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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