In polar coordinates the Laplacian is given by
\[\Delta u = \partial_r^2 u + \frac{d-1}{r} \partial_r u + \frac{1}{r^2} \Delta_{\mathbb{S}^{d-1}} u,\]where \(\Delta_{\mathbb{S}^{d-1}}\) denotes the spherical Laplacian.
In polar coordinates the Laplacian is given by
\[\Delta u = \partial_r^2 u + \frac{d-1}{r} \partial_r u + \frac{1}{r^2} \Delta_{\mathbb{S}^{d-1}} u,\]where \(\Delta_{\mathbb{S}^{d-1}}\) denotes the spherical Laplacian.