Why $\int_{B_r}u(y)dy=\int_{\partial B_r}\partial _r u(y)dy$?

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Let here the proof. Can anyone tells me where (1.2.4) come from ? In what an integration by part can allow us to conclude ? I really don't see how it works. By the way, does the symbol $\int$ with the $-$ has a special meaning or it's just to specify $\oint$ ?

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