I want to whow that
$ 2 \int_{\partial B} ( \nabla g) (x+ tz) z dz = 3t \int_{B} ( \Delta g)(x+tz) dz $ Here, $ B$ is a unit sphere in $R^3$.
$ x = (x_1, x_2, x_3), t \geqslant 0 $ $ \nabla = \left ( \frac{\partial}{\partial x_1}, \frac{\partial}{\partial x_2} , \frac{\partial}{\partial x_3} \right) $ $ \Delta = \sum_{j=1}^3 \frac{\partial^2}{\partial x_j^2} $