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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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    @WillieWong : Thank you .2012-07-10

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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).